LMFDB - Embedded newform 738.2.v.a.137.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(137,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.137"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([4, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.v (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [168,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$21$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			137.3
Character	$\chi$	$=$	738.137
Dual form			738.2.v.a.167.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{2} +(-1.68221 - 0.412525i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.872167 - 3.25497i) q^{5} +(-0.0369189 - 1.73166i) q^{6} +(2.62871 + 0.346077i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.65965 + 1.38791i) q^{9} +3.36980 q^{10} +(-1.81231 - 0.238596i) q^{11} +(1.66310 - 0.483847i) q^{12} +(-0.549181 + 0.715707i) q^{13} +(0.346077 + 2.62871i) q^{14} +(-2.80992 + 5.11575i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-6.44629 - 2.67014i) q^{17} +(-0.652247 + 2.92824i) q^{18} +(1.57542 - 3.80341i) q^{19} +(0.872167 + 3.25497i) q^{20} +(-4.27928 - 1.66658i) q^{21} +(-0.238596 - 1.81231i) q^{22} +(0.394630 + 0.683520i) q^{23} +(0.897801 + 1.48120i) q^{24} +(-5.50404 - 3.17776i) q^{25} +(-0.833458 - 0.345230i) q^{26} +(-3.90153 - 3.43192i) q^{27} +(-2.44957 + 1.01465i) q^{28} +(0.520557 - 3.95402i) q^{29} +(-5.66870 - 1.39012i) q^{30} +(8.28363 - 4.78256i) q^{31} +(0.965926 + 0.258819i) q^{32} +(2.95026 + 1.14899i) q^{33} +(0.910736 - 6.91773i) q^{34} +(3.41915 - 8.25455i) q^{35} +(-2.99727 + 0.127862i) q^{36} -6.35886 q^{37} +(4.08156 + 0.537348i) q^{38} +(1.21908 - 0.977417i) q^{39} +(-2.91833 + 1.68490i) q^{40} +(-2.27555 + 5.98514i) q^{41} +(0.502237 - 4.56481i) q^{42} +(4.05897 - 1.08760i) q^{43} +(1.68881 - 0.699527i) q^{44} +(6.83725 - 7.44659i) q^{45} +(-0.558092 + 0.558092i) q^{46} +(9.16755 - 7.03451i) q^{47} +(-1.19836 + 1.25057i) q^{48} +(0.0288824 + 0.00773902i) q^{49} +(1.64493 - 6.13896i) q^{50} +(9.74251 + 7.15099i) q^{51} +(0.117751 - 0.894411i) q^{52} +(-5.50514 - 13.2906i) q^{53} +(2.30519 - 4.65684i) q^{54} +(-2.35726 + 5.69094i) q^{55} +(-1.61407 - 2.10349i) q^{56} +(-4.21919 + 5.74823i) q^{57} +(3.95402 - 0.520557i) q^{58} +(-5.12647 + 2.95977i) q^{59} +(-0.124409 - 5.83533i) q^{60} +(-2.60605 + 0.698289i) q^{61} +(6.76356 + 6.76356i) q^{62} +(6.51113 + 4.56885i) q^{63} +1.00000i q^{64} +(1.85063 + 2.41179i) q^{65} +(-0.346257 + 3.14712i) q^{66} +(-3.21244 + 0.422926i) q^{67} +(6.91773 - 0.910736i) q^{68} +(-0.381881 - 1.31262i) q^{69} +(8.85823 + 1.16621i) q^{70} +(-0.572841 + 0.237279i) q^{71} +(-0.899257 - 2.86205i) q^{72} +(7.43536 + 7.43536i) q^{73} +(-1.64579 - 6.14219i) q^{74} +(7.94804 + 7.61621i) q^{75} +(0.537348 + 4.08156i) q^{76} +(-4.68148 - 1.25440i) q^{77} +(1.25963 + 0.924571i) q^{78} +(1.76414 - 13.4000i) q^{79} +(-2.38281 - 2.38281i) q^{80} +(5.14744 + 7.38268i) q^{81} +(-6.37016 - 0.648940i) q^{82} +(-8.58655 - 4.95745i) q^{83} +(4.53925 - 0.696335i) q^{84} +(-14.3135 + 18.6537i) q^{85} +(2.10108 + 3.63918i) q^{86} +(-2.50682 + 6.43674i) q^{87} +(1.11279 + 1.45021i) q^{88} +(5.56027 - 2.30314i) q^{89} +(8.96246 + 4.67696i) q^{90} +(-1.69133 + 1.69133i) q^{91} +(-0.683520 - 0.394630i) q^{92} +(-15.9077 + 4.62805i) q^{93} +(9.16755 + 7.03451i) q^{94} +(-11.0060 - 8.44518i) q^{95} +(-1.51812 - 0.833856i) q^{96} +(-5.41524 + 4.15526i) q^{97} +0.0299013i q^{98} +(-4.48897 - 3.14990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 4 q^{3} - 12 q^{7} - 4 q^{9} + 8 q^{15} + 84 q^{16} - 12 q^{17} - 8 q^{21} - 12 q^{22} + 48 q^{25} - 40 q^{27} + 16 q^{30} - 64 q^{33} - 36 q^{34} + 24 q^{35} - 4 q^{36} + 32 q^{39} - 32 q^{42}+ \cdots + 68 q^{99}+O(q^{100}) $ 168 * q - 4 * q^3 - 12 * q^7 - 4 * q^9 + 8 * q^15 + 84 * q^16 - 12 * q^17 - 8 * q^21 - 12 * q^22 + 48 * q^25 - 40 * q^27 + 16 * q^30 - 64 * q^33 - 36 * q^34 + 24 * q^35 - 4 * q^36 + 32 * q^39 - 32 * q^42 + 12 * q^44 + 72 * q^45 - 12 * q^47 - 8 * q^48 + 12 * q^49 - 44 * q^51 + 12 * q^56 - 64 * q^57 - 24 * q^58 - 108 * q^61 + 48 * q^63 - 84 * q^65 - 4 * q^66 - 60 * q^67 + 40 * q^69 + 12 * q^70 + 20 * q^75 - 60 * q^79 + 68 * q^81 + 12 * q^82 - 120 * q^83 + 8 * q^84 + 24 * q^85 + 72 * q^89 + 40 * q^90 - 16 * q^93 - 12 * q^94 - 120 * q^95 + 96 * q^97 + 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−1.68221	−	0.412525i	−0.971223	−	0.238171i
$3$	−1.68221	−	0.412525i	−0.971223	−	0.238171i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.872167	−	3.25497i	0.390045	−	1.45567i	−0.440013	−	0.897991i	$-0.645026\pi$
$5$	0.872167	−	3.25497i	0.390045	−	1.45567i	0.830058	−	0.557677i	$-0.188307\pi$
$6$	−0.0369189	−	1.73166i	−0.0150721	−	0.706946i
$7$	2.62871	+	0.346077i	0.993560	+	0.130805i	0.609739	−	0.792603i	$-0.291274\pi$
$7$	2.62871	+	0.346077i	0.993560	+	0.130805i	0.383822	+	0.923407i	$0.374608\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.65965	+	1.38791i	0.886549	+	0.462635i
$10$	3.36980			1.06562
$11$	−1.81231	−	0.238596i	−0.546433	−	0.0719393i	−0.147744	−	0.989026i	$-0.547201\pi$
$11$	−1.81231	−	0.238596i	−0.546433	−	0.0719393i	−0.398689	+	0.917086i	$0.630535\pi$
$12$	1.66310	−	0.483847i	0.480095	−	0.139675i
$13$	−0.549181	+	0.715707i	−0.152315	+	0.198501i	−0.863278	−	0.504728i	$-0.831593\pi$
$13$	−0.549181	+	0.715707i	−0.152315	+	0.198501i	0.710963	+	0.703230i	$0.248259\pi$
$14$	0.346077	+	2.62871i	0.0924929	+	0.702553i
$15$	−2.80992	+	5.11575i	−0.725519	+	1.32088i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−6.44629	−	2.67014i	−1.56346	−	0.647605i	−0.577770	−	0.816199i	$-0.696077\pi$
$17$	−6.44629	−	2.67014i	−1.56346	−	0.647605i	−0.985685	+	0.168595i	$0.946077\pi$
$18$	−0.652247	+	2.92824i	−0.153736	+	0.690192i
$19$	1.57542	−	3.80341i	0.361427	−	0.872563i	−0.633665	−	0.773608i	$-0.718450\pi$
$19$	1.57542	−	3.80341i	0.361427	−	0.872563i	0.995092	−	0.0989547i	$-0.0315499\pi$
$20$	0.872167	+	3.25497i	0.195023	+	0.727834i
$21$	−4.27928	−	1.66658i	−0.933815	−	0.363678i
$22$	−0.238596	−	1.81231i	−0.0508688	−	0.386387i
$23$	0.394630	+	0.683520i	0.0822861	+	0.142524i	0.904232	−	0.427042i	$-0.140445\pi$
$23$	0.394630	+	0.683520i	0.0822861	+	0.142524i	−0.821945	+	0.569566i	$0.807111\pi$
$24$	0.897801	+	1.48120i	0.183263	+	0.302349i
$25$	−5.50404	−	3.17776i	−1.10081	−	0.635552i
$26$	−0.833458	−	0.345230i	−0.163455	−	0.0677051i
$27$	−3.90153	−	3.43192i	−0.750850	−	0.660473i
$28$	−2.44957	+	1.01465i	−0.462925	+	0.191750i
$29$	0.520557	−	3.95402i	0.0966650	−	0.734244i	−0.872637	−	0.488370i	$-0.837592\pi$
$29$	0.520557	−	3.95402i	0.0966650	−	0.734244i	0.969302	−	0.245874i	$-0.0790749\pi$
$30$	−5.66870	−	1.39012i	−1.03496	−	0.253801i
$31$	8.28363	−	4.78256i	1.48778	−	0.858973i	0.487881	−	0.872910i	$-0.337770\pi$
$31$	8.28363	−	4.78256i	1.48778	−	0.858973i	0.999903	+	0.0139373i	$0.00443653\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	2.95026	+	1.14899i	0.513575	+	0.200014i
$34$	0.910736	−	6.91773i	0.156190	−	1.18638i
$35$	3.41915	−	8.25455i	0.577941	−	1.39527i
$36$	−2.99727	+	0.127862i	−0.499546	+	0.0213103i
$37$	−6.35886			−1.04539			−0.522695	−	0.852520i	$-0.675073\pi$
$37$	−6.35886			−1.04539			−0.522695	+	0.852520i	$0.675073\pi$
$38$	4.08156	+	0.537348i	0.662117	+	0.0871694i
$39$	1.21908	−	0.977417i	0.195210	−	0.156512i
$40$	−2.91833	+	1.68490i	−0.461428	+	0.266406i
$41$	−2.27555	+	5.98514i	−0.355381	+	0.934722i
$41$	−2.27555	+	5.98514i	−0.355381	+	0.934722i
$42$	0.502237	−	4.56481i	0.0774968	−	0.704365i
$43$	4.05897	−	1.08760i	0.618988	−	0.165857i	0.0643201	−	0.997929i	$-0.479512\pi$
$43$	4.05897	−	1.08760i	0.618988	−	0.165857i	0.554667	+	0.832072i	$0.312845\pi$
$44$	1.68881	−	0.699527i	0.254597	−	0.105458i
$45$	6.83725	−	7.44659i	1.01924	−	1.11007i
$46$	−0.558092	+	0.558092i	−0.0822861	+	0.0822861i
$47$	9.16755	−	7.03451i	1.33722	−	1.02609i	0.340929	−	0.940089i	$-0.389258\pi$
$47$	9.16755	−	7.03451i	1.33722	−	1.02609i	0.996295	−	0.0859991i	$-0.0274082\pi$
$48$	−1.19836	+	1.25057i	−0.172969	+	0.180505i
$49$	0.0288824	+	0.00773902i	0.00412606	+	0.00110557i
$50$	1.64493	−	6.13896i	0.232628	−	0.868181i
$51$	9.74251	+	7.15099i	1.36422	+	1.00134i
$52$	0.117751	−	0.894411i	0.0163292	−	0.124032i
$53$	−5.50514	−	13.2906i	−0.756189	−	1.82560i	−0.520742	−	0.853714i	$-0.674345\pi$
$53$	−5.50514	−	13.2906i	−0.756189	−	1.82560i	−0.235447	−	0.971887i	$-0.575655\pi$
$54$	2.30519	−	4.65684i	0.313696	−	0.633715i
$55$	−2.35726	+	5.69094i	−0.317853	+	0.767366i
$56$	−1.61407	−	2.10349i	−0.215689	−	0.281091i
$57$	−4.21919	+	5.74823i	−0.558846	+	0.761371i
$58$	3.95402	−	0.520557i	0.519189	−	0.0683525i
$59$	−5.12647	+	2.95977i	−0.667409	+	0.385329i	−0.795094	−	0.606486i	$-0.792579\pi$
$59$	−5.12647	+	2.95977i	−0.667409	+	0.385329i	0.127685	+	0.991815i	$0.459245\pi$
$60$	−0.124409	−	5.83533i	−0.0160612	−	0.753338i
$61$	−2.60605	+	0.698289i	−0.333670	+	0.0894067i	−0.421764	−	0.906705i	$-0.638589\pi$
$61$	−2.60605	+	0.698289i	−0.333670	+	0.0894067i	0.0880941	+	0.996112i	$0.471922\pi$
$62$	6.76356	+	6.76356i	0.858973	+	0.858973i
$63$	6.51113	+	4.56885i	0.820325	+	0.575621i
$64$			1.00000i			0.125000i
$65$	1.85063	+	2.41179i	0.229542	+	0.299145i
$66$	−0.346257	+	3.14712i	−0.0426213	+	0.387383i
$67$	−3.21244	+	0.422926i	−0.392462	+	0.0516686i	−0.324175	−	0.945997i	$-0.605087\pi$
$67$	−3.21244	+	0.422926i	−0.392462	+	0.0516686i	−0.0682870	+	0.997666i	$0.521753\pi$
$68$	6.91773	−	0.910736i	0.838897	−	0.110443i
$69$	−0.381881	−	1.31262i	−0.0459731	−	0.158021i
$70$	8.85823	+	1.16621i	1.05876	+	0.139388i
$71$	−0.572841	+	0.237279i	−0.0679837	+	0.0281598i	−0.416416	−	0.909174i	$-0.636714\pi$
$71$	−0.572841	+	0.237279i	−0.0679837	+	0.0281598i	0.348432	+	0.937334i	$0.386714\pi$
$72$	−0.899257	−	2.86205i	−0.105978	−	0.337296i
$73$	7.43536	+	7.43536i	0.870243	+	0.870243i	0.992499	−	0.122256i	$-0.0390128\pi$
$73$	7.43536	+	7.43536i	0.870243	+	0.870243i	−0.122256	+	0.992499i	$0.539013\pi$
$74$	−1.64579	−	6.14219i	−0.191320	−	0.714015i
$75$	7.94804	+	7.61621i	0.917761	+	0.879444i
$76$	0.537348	+	4.08156i	0.0616380	+	0.468187i
$77$	−4.68148	−	1.25440i	−0.533504	−	0.142952i
$78$	1.25963	+	0.924571i	0.142626	+	0.104687i
$79$	1.76414	−	13.4000i	0.198481	−	1.50761i	−0.544761	−	0.838591i	$-0.683380\pi$
$79$	1.76414	−	13.4000i	0.198481	−	1.50761i	0.743242	−	0.669023i	$-0.233287\pi$
$80$	−2.38281	−	2.38281i	−0.266406	−	0.266406i
$81$	5.14744	+	7.38268i	0.571937	+	0.820297i
$82$	−6.37016	−	0.648940i	−0.703466	−	0.0716635i
$83$	−8.58655	−	4.95745i	−0.942497	−	0.544151i	−0.0517545	−	0.998660i	$-0.516481\pi$
$83$	−8.58655	−	4.95745i	−0.942497	−	0.544151i	−0.890742	+	0.454509i	$0.849815\pi$
$84$	4.53925	−	0.696335i	0.495273	−	0.0759764i
$85$	−14.3135	+	18.6537i	−1.55252	+	2.02328i
$86$	2.10108	+	3.63918i	0.226565	+	0.392422i
$87$	−2.50682	+	6.43674i	−0.268759	+	0.690091i
$88$	1.11279	+	1.45021i	0.118623	+	0.154593i
$89$	5.56027	−	2.30314i	0.589387	−	0.244132i	−0.0679997	−	0.997685i	$-0.521662\pi$
$89$	5.56027	−	2.30314i	0.589387	−	0.244132i	0.657387	+	0.753553i	$0.271662\pi$
$90$	8.96246	+	4.67696i	0.944727	+	0.492995i
$91$	−1.69133	+	1.69133i	−0.177300	+	0.177300i
$92$	−0.683520	−	0.394630i	−0.0712619	−	0.0411431i
$93$	−15.9077	+	4.62805i	−1.64955	+	0.479906i
$94$	9.16755	+	7.03451i	0.945560	+	0.725554i
$95$	−11.0060	−	8.44518i	−1.12919	−	0.866457i
$96$	−1.51812	−	0.833856i	−0.154942	−	0.0851051i
$97$	−5.41524	+	4.15526i	−0.549834	+	0.421903i	−0.845960	−	0.533246i	$-0.820972\pi$
$97$	−5.41524	+	4.15526i	−0.549834	+	0.421903i	0.296126	+	0.955149i	$0.404305\pi$
$98$			0.0299013i			0.00302049i
$99$	−4.48897	−	3.14990i	−0.451158	−	0.316577i
$100$	6.35552			0.635552
$101$	11.1852	−	8.58274i	1.11297	−	0.854015i	0.122603	−	0.992456i	$-0.460876\pi$
$101$	11.1852	−	8.58274i	1.11297	−	0.854015i	0.990371	+	0.138441i	$0.0442091\pi$
$102$	−4.38578	+	11.2614i	−0.434257	+	1.11504i
$103$	3.92783	+	1.05246i	0.387020	+	0.103702i	0.447082	−	0.894493i	$-0.352463\pi$
$103$	3.92783	+	1.05246i	0.387020	+	0.103702i	−0.0600618	+	0.998195i	$0.519130\pi$
$104$	0.894411	−	0.117751i	0.0877042	−	0.0115465i
$105$	−9.15693	+	12.4754i	−0.893624	+	1.21747i
$106$	11.4129	−	8.75741i	1.10852	−	0.850595i
$107$	2.79045			0.269763			0.134881	−	0.990862i	$-0.456935\pi$
$107$	2.79045			0.269763			0.134881	+	0.990862i	$0.456935\pi$
$108$	5.09478	+	1.02136i	0.490246	+	0.0982804i
$109$	8.49392	+	3.51830i	0.813570	+	0.336992i	0.750377	−	0.661010i	$-0.229872\pi$
$109$	8.49392	+	3.51830i	0.813570	+	0.336992i	0.0631925	+	0.998001i	$0.479872\pi$
$110$	−6.10713	−	0.804019i	−0.582292	−	0.0766602i
$111$	10.6969	+	2.62319i	1.01531	+	0.248982i
$112$	1.61407	−	2.10349i	0.152515	−	0.198761i
$113$	−0.711501	−	1.23236i	−0.0669323	−	0.115930i	0.830617	−	0.556844i	$-0.187988\pi$
$113$	−0.711501	−	1.23236i	−0.0669323	−	0.115930i	−0.897550	+	0.440914i	$0.854655\pi$
$114$	−6.64437	−	2.58768i	−0.622302	−	0.242358i
$115$	2.56902	−	0.688367i	0.239563	−	0.0641906i
$116$	1.52620	+	3.68456i	0.141704	+	0.342103i
$117$	−2.45396	+	1.14132i	−0.226869	+	0.105515i
$118$	−4.18574	−	4.18574i	−0.385329	−	0.385329i
$119$	−16.0214	−	9.24995i	−1.46868	−	0.847941i
$120$	5.60430	−	1.63046i	0.511600	−	0.148840i
$121$	−7.39763	−	1.98219i	−0.672512	−	0.180199i
$122$	−1.34899	−	2.33652i	−0.122132	−	0.211538i
$123$	6.29696	−	9.12953i	0.567778	−	0.823182i
$124$	−4.78256	+	8.28363i	−0.429486	+	0.743892i
$125$	−3.22995	+	3.22995i	−0.288895	+	0.288895i
$126$	−2.72796	+	7.47177i	−0.243026	+	0.665638i
$127$			12.5448i			1.11317i	0.830789	+	0.556587i	$0.187889\pi$
$127$			12.5448i			1.11317i	−0.830789	+	0.556587i	$0.812111\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−7.27670	+	0.155139i	−0.640677	+	0.0136592i
$130$	−1.85063	+	2.41179i	−0.162311	+	0.211528i
$131$	−4.55568	+	17.0020i	−0.398032	+	1.48548i	0.418522	+	0.908207i	$0.362548\pi$
$131$	−4.55568	+	17.0020i	−0.398032	+	1.48548i	−0.816554	+	0.577269i	$0.804118\pi$
$132$	−3.12950	+	0.480075i	−0.272388	+	0.0417851i
$133$	5.45761	−	9.45286i	0.473235	−	0.819667i
$134$	−1.23996	−	2.99352i	−0.107116	−	0.258601i
$135$	−14.5736	+	9.70618i	−1.25429	+	0.835375i
$136$	2.67014	+	6.44629i	0.228963	+	0.552765i
$137$	−9.09199	+	6.97653i	−0.776781	+	0.596045i	−0.919213	−	0.393760i	$-0.871174\pi$
$137$	−9.09199	+	6.97653i	−0.776781	+	0.596045i	0.142433	+	0.989805i	$0.454508\pi$
$138$	1.16905	−	0.708599i	0.0995164	−	0.0603200i
$139$	4.96716	+	8.60337i	0.421309	+	0.729728i	0.996068	−	0.0885946i	$-0.0282376\pi$
$139$	4.96716	+	8.60337i	0.421309	+	0.729728i	−0.574759	+	0.818323i	$0.694904\pi$
$140$	1.16621	+	8.85823i	0.0985625	+	0.748657i
$141$	−18.3236	+	8.05166i	−1.54313	+	0.678072i
$142$	−0.377456	−	0.491910i	−0.0316754	−	0.0412802i
$143$	1.16605	−	1.16605i	0.0975103	−	0.0975103i
$144$	2.53178	−	1.60937i	0.210982	−	0.134114i
$145$	−12.4162	−	5.14297i	−1.03111	−	0.427100i
$146$	−5.25759	+	9.10642i	−0.435121	+	0.753652i
$147$	−0.0453937	−	0.0249334i	−0.00374401	−	0.00205647i
$148$	5.50694	−	3.17943i	0.452667	−	0.261348i
$149$	−1.50110	−	11.4020i	−0.122975	−	0.934086i	−0.936035	−	0.351906i	$-0.885534\pi$
$149$	−1.50110	−	11.4020i	−0.122975	−	0.934086i	0.813061	−	0.582179i	$-0.197800\pi$
$150$	−5.29959	+	9.64844i	−0.432710	+	0.787792i
$151$	−0.725499	+	5.51071i	−0.0590403	+	0.448456i	0.936236	+	0.351372i	$0.114285\pi$
$151$	−0.725499	+	5.51071i	−0.0590403	+	0.448456i	−0.995276	+	0.0970836i	$0.969049\pi$
$152$	−3.80341	+	1.57542i	−0.308497	+	0.127784i
$153$	−13.4390	−	16.0485i	−1.08648	−	1.29744i
$154$		−	4.84663i		−	0.390552i
$155$	−8.34238	−	31.1342i	−0.670076	−	2.50076i
$156$	−0.567049	+	1.45601i	−0.0454003	+	0.116574i
$157$	8.28430	+	6.35677i	0.661159	+	0.507325i	0.883974	−	0.467535i	$-0.154858\pi$
$157$	8.28430	+	6.35677i	0.661159	+	0.507325i	−0.222815	+	0.974861i	$0.571525\pi$
$158$	13.4000	−	1.76414i	1.06604	−	0.140347i
$159$	3.77809	+	24.6285i	0.299622	+	1.95317i
$160$	1.68490	−	2.91833i	0.133203	−	0.230714i
$161$	0.800820	+	1.93335i	0.0631134	+	0.152369i
$162$	−5.79886	+	6.88282i	−0.455602	+	0.540765i
$163$			1.23582i			0.0967968i	0.998828	+	0.0483984i	$0.0154117\pi$
$163$			1.23582i			0.0967968i	−0.998828	+	0.0483984i	$0.984588\pi$
$164$	−1.02189	−	6.32106i	−0.0797961	−	0.493592i
$165$	6.31306	−	8.60091i	0.491471	−	0.669580i
$166$	2.56616	−	9.57705i	0.199173	−	0.743324i
$167$	13.8207	+	10.6050i	1.06948	+	0.820638i	0.984437	−	0.175739i	$-0.0562315\pi$
$167$	13.8207	+	10.6050i	1.06948	+	0.820638i	0.0850400	+	0.996378i	$0.472898\pi$
$168$	1.84745	+	4.20436i	0.142534	+	0.324373i
$169$	3.15401	+	11.7709i	0.242616	+	0.905456i
$170$	−21.7227	−	8.99783i	−1.66605	−	0.690102i
$171$	9.46885	−	7.92919i	0.724101	−	0.606360i
$172$	−2.97137	+	2.97137i	−0.226565	+	0.226565i
$173$	19.5055	−	5.22647i	1.48297	−	0.397361i	0.575615	−	0.817721i	$-0.304763\pi$
$173$	19.5055	−	5.22647i	1.48297	−	0.397361i	0.907358	+	0.420360i	$0.138096\pi$
$174$	−6.86623	−	0.755448i	−0.520528	−	0.0572704i
$175$	−13.3688	−	10.2582i	−1.01059	−	0.775450i
$176$	−1.11279	+	1.45021i	−0.0838795	+	0.109314i
$177$	9.84476	−	2.86415i	0.739977	−	0.215282i
$178$	3.66376	+	4.77471i	0.274611	+	0.357880i
$179$	3.10978	−	7.50768i	0.232436	−	0.561151i	−0.764027	−	0.645185i	$-0.776780\pi$
$179$	3.10978	−	7.50768i	0.232436	−	0.561151i	0.996463	+	0.0840340i	$0.0267804\pi$
$180$	−2.19794	+	9.86756i	−0.163825	+	0.735485i
$181$	3.58592	−	8.65717i	0.266539	−	0.643482i	−0.732777	−	0.680469i	$-0.761776\pi$
$181$	3.58592	−	8.65717i	0.266539	−	0.643482i	0.999316	+	0.0369869i	$0.0117760\pi$
$182$	−2.07145	−	1.19595i	−0.153546	−	0.0886498i
$183$	4.67198	−	0.0996065i	0.345362	−	0.00736312i
$184$	0.204276	−	0.762367i	0.0150594	−	0.0562025i
$185$	−5.54599	+	20.6979i	−0.407749	+	1.52174i
$186$	−8.58757	−	14.1678i	−0.629671	−	1.03884i
$187$	11.0456	+	6.37719i	0.807736	+	0.466347i
$188$	−4.42208	+	10.6758i	−0.322513	+	0.778615i
$189$	−9.06830	−	10.3718i	−0.659622	−	0.754434i
$190$	5.30886	−	12.8167i	0.385145	−	0.929823i
$191$	11.8112	+	15.3926i	0.854627	+	1.11377i	0.992369	+	0.123303i	$0.0393489\pi$
$191$	11.8112	+	15.3926i	0.854627	+	1.11377i	−0.137742	+	0.990468i	$0.543984\pi$
$192$	0.412525	−	1.68221i	0.0297714	−	0.121403i
$193$	−2.28445	+	2.97716i	−0.164438	+	0.214300i	−0.868303	−	0.496033i	$-0.834789\pi$
$193$	−2.28445	+	2.97716i	−0.164438	+	0.214300i	0.703865	+	0.710334i	$0.251456\pi$
$194$	−5.41524	−	4.15526i	−0.388792	−	0.298330i
$195$	−2.11822	−	4.82056i	−0.151689	−	0.345207i
$196$	−0.0288824	+	0.00773902i	−0.00206303	+	0.000552787i
$197$	−15.1676	+	15.1676i	−1.08065	+	1.08065i	−0.0841995	+	0.996449i	$0.526833\pi$
$197$	−15.1676	+	15.1676i	−1.08065	+	1.08065i	−0.996449	+	0.0841995i	$0.973167\pi$
$198$	1.88074	−	5.15126i	0.133658	−	0.366084i
$199$	14.8839	+	6.16510i	1.05509	+	0.437032i	0.841706	−	0.539936i	$-0.181552\pi$
$199$	14.8839	+	6.16510i	1.05509	+	0.437032i	0.213384	+	0.976969i	$0.431552\pi$
$200$	1.64493	+	6.13896i	0.116314	+	0.434090i
$201$	5.57846	+	0.613763i	0.393474	+	0.0432915i
$202$	11.1852	+	8.58274i	0.786991	+	0.603880i
$203$	2.73679	−	10.2138i	0.192085	−	0.716871i
$204$	−12.0128	−	1.32169i	−0.841061	−	0.0925366i
$205$	17.4968	+	12.6269i	1.22203	+	0.881900i
$206$			4.06639i			0.283319i
$207$	0.100916	+	2.36563i	0.00701417	+	0.164423i
$208$	0.345230	+	0.833458i	0.0239374	+	0.0577899i
$209$	−3.76264	+	6.51709i	−0.260267	+	0.450796i
$210$	−14.4203	−	5.61604i	−0.995094	−	0.387544i
$211$	−2.91998	+	0.384422i	−0.201019	+	0.0264647i	−0.230363	−	0.973105i	$-0.573992\pi$
$211$	−2.91998	+	0.384422i	−0.201019	+	0.0264647i	0.0293440	+	0.999569i	$0.490658\pi$
$212$	11.4129	+	8.75741i	0.783840	+	0.601461i
$213$	1.06152	−	0.162841i	0.0727342	−	0.0111577i
$214$	0.722222	+	2.69537i	0.0493701	+	0.184252i
$215$		−	14.1604i		−	0.965732i
$216$	0.332069	+	5.18553i	0.0225944	+	0.352831i
$217$	23.4304	−	9.70520i	1.59056	−	0.658832i
$218$	−1.20003	+	9.11510i	−0.0812760	+	0.617352i
$219$	−9.44055	−	15.5751i	−0.637933	−	1.05247i
$220$	−0.804019	−	6.10713i	−0.0542069	−	0.411742i
$221$	5.45122	−	3.14727i	0.366689	−	0.211708i
$222$	0.234762	+	11.0114i	0.0157562	+	0.739035i
$223$	6.86446	−	11.8896i	0.459679	−	0.796187i	−0.539265	−	0.842136i	$-0.681298\pi$
$223$	6.86446	−	11.8896i	0.459679	−	0.796187i	0.998944	+	0.0459494i	$0.0146313\pi$
$224$	2.44957	+	1.01465i	0.163669	+	0.0677938i
$225$	−10.2284	−	16.0908i	−0.681892	−	1.07272i
$226$	1.00621	−	1.00621i	0.0669323	−	0.0669323i
$227$	4.74888	+	6.18887i	0.315195	+	0.410769i	0.923904	−	0.382623i	$-0.124979\pi$
$227$	4.74888	+	6.18887i	0.315195	+	0.410769i	−0.608710	+	0.793393i	$0.708313\pi$
$228$	0.779816	−	7.08771i	0.0516446	−	0.469395i
$229$	0.289840	+	2.20155i	0.0191532	+	0.145483i	0.998349	−	0.0574330i	$-0.0182916\pi$
$229$	0.289840	+	2.20155i	0.0191532	+	0.145483i	−0.979196	+	0.202916i	$0.934958\pi$
$230$	1.32982	+	2.30332i	0.0876860	+	0.151877i
$231$	7.35775	+	4.04139i	0.484105	+	0.265904i
$232$	−3.16401	+	2.42783i	−0.207727	+	0.159395i
$233$	1.84353	+	4.45067i	0.120773	+	0.291573i	0.972691	−	0.232102i	$-0.0745605\pi$
$233$	1.84353	+	4.45067i	0.120773	+	0.291573i	−0.851918	+	0.523675i	$0.824560\pi$
$234$	−1.73756	−	2.07495i	−0.113588	−	0.135644i
$235$	−14.9015	−	35.9754i	−0.972066	−	2.34678i
$236$	2.95977	−	5.12647i	0.192664	−	0.333704i
$237$	−8.49547	+	21.8138i	−0.551840	+	1.41696i
$238$	4.78813	−	17.8695i	0.310368	−	1.15831i
$239$	−12.5033	+	16.2946i	−0.808769	+	1.05401i	0.188638	+	0.982047i	$0.439593\pi$
$239$	−12.5033	+	16.2946i	−0.808769	+	1.05401i	−0.997407	+	0.0719619i	$0.977074\pi$
$240$	3.02541	+	4.99134i	0.195289	+	0.322190i
$241$	−10.4805	+	2.80823i	−0.675106	+	0.180894i	−0.580054	−	0.814578i	$-0.696968\pi$
$241$	−10.4805	+	2.80823i	−0.675106	+	0.180894i	−0.0950522	+	0.995472i	$0.530302\pi$
$242$		−	7.65859i		−	0.492313i
$243$	−5.61352	−	14.5426i	−0.360108	−	0.932911i
$244$	1.90776	−	1.90776i	0.122132	−	0.122132i
$245$	0.0503806	−	0.0872618i	0.00321870	−	0.00557495i
$246$	10.4482	+	3.71950i	0.666154	+	0.237147i
$247$	1.85693	+	3.21630i	0.118154	+	0.204649i
$248$	−9.23919	−	2.47563i	−0.586689	−	0.157203i
$249$	12.3993	+	11.8816i	0.785773	+	0.752967i
$250$	−3.95586	−	2.28392i	−0.250191	−	0.144448i
$251$	5.65353	+	5.65353i	0.356848	+	0.356848i	0.862650	−	0.505802i	$-0.168803\pi$
$251$	5.65353	+	5.65353i	0.356848	+	0.356848i	−0.505802	+	0.862650i	$0.668803\pi$
$252$	−7.92322	−	0.701175i	−0.499116	−	0.0441698i
$253$	−0.552109	−	1.33291i	−0.0347108	−	0.0837993i
$254$	−12.1174	+	3.24684i	−0.760312	+	0.203725i
$255$	31.7734	−	25.4747i	1.98973	−	1.59529i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.5791	+	18.9998i	−0.909417	+	1.18518i	0.0727850	+	0.997348i	$0.476811\pi$
$257$	−14.5791	+	18.9998i	−0.909417	+	1.18518i	−0.982202	+	0.187828i	$0.939855\pi$
$258$	−2.03320	−	6.98860i	−0.126582	−	0.435091i
$259$	−16.7156	−	2.20065i	−1.03866	−	0.136742i
$260$	−2.80858	−	1.16335i	−0.174181	−	0.0721481i
$261$	6.87231	−	9.79382i	0.425385	−	0.606222i
$262$	−17.6018			−1.08744
$263$	17.1361	−	13.1490i	1.05665	−	0.810800i	0.0741891	−	0.997244i	$-0.476363\pi$
$263$	17.1361	−	13.1490i	1.05665	−	0.810800i	0.982465	+	0.186445i	$0.0596965\pi$
$264$	−1.27369	−	2.89861i	−0.0783902	−	0.178397i
$265$	−48.0619	+	6.32746i	−2.95242	+	0.388693i
$266$	10.5433	+	2.82507i	0.646451	+	0.173216i
$267$	−10.3036	+	1.58061i	−0.630572	+	0.0967317i
$268$	2.57059	−	1.97248i	0.157024	−	0.120489i
$269$	22.9668			1.40031			0.700156	−	0.713990i	$-0.253114\pi$
$269$	22.9668			1.40031			0.700156	+	0.713990i	$0.253114\pi$
$270$	−13.1474	−	11.5649i	−0.800123	−	0.703815i
$271$		−	12.8426i		−	0.780133i	−0.920787	−	0.390067i	$-0.872452\pi$
$271$		−	12.8426i		−	0.780133i	0.920787	−	0.390067i	$-0.127548\pi$
$272$	−5.53556	+	4.24758i	−0.335643	+	0.257548i
$273$	3.54288	−	2.14745i	0.214425	−	0.129970i
$274$	−9.09199	−	6.97653i	−0.549267	−	0.421467i
$275$	9.21686	+	7.07234i	0.555797	+	0.426478i
$276$	0.987028	+	0.945819i	0.0594121	+	0.0569316i
$277$	−15.2368	−	8.79696i	−0.915490	−	0.528558i	−0.0332963	−	0.999446i	$-0.510601\pi$
$277$	−15.2368	−	8.79696i	−0.915490	−	0.528558i	−0.882193	+	0.470887i	$0.843934\pi$
$278$	−7.02462	+	7.02462i	−0.421309	+	0.421309i
$279$	28.6693	−	1.22301i	1.71638	−	0.0732199i
$280$	−8.25455	+	3.41915i	−0.493304	+	0.204333i
$281$	−6.92575	−	9.02582i	−0.413156	−	0.538435i	0.539701	−	0.841857i	$-0.318537\pi$
$281$	−6.92575	−	9.02582i	−0.413156	−	0.538435i	−0.952856	+	0.303422i	$0.901871\pi$
$282$	−12.5198	−	15.6153i	−0.745544	−	0.929880i
$283$	6.57212	+	11.3832i	0.390672	+	0.676664i	0.992538	−	0.121933i	$-0.0389093\pi$
$283$	6.57212	+	11.3832i	0.390672	+	0.676664i	−0.601866	+	0.798597i	$0.705576\pi$
$284$	0.377456	−	0.491910i	0.0223979	−	0.0291895i
$285$	15.0305	+	18.7468i	0.890329	+	1.11046i
$286$	1.42812	+	0.824524i	0.0844464	+	0.0487551i
$287$	−8.05307	+	14.9457i	−0.475358	+	0.882217i
$288$	2.20980	+	2.02898i	0.130214	+	0.119559i
$289$	22.4042	+	22.4042i	1.31790	+	1.31790i
$290$	1.75417	−	13.3242i	0.103008	−	0.782427i
$291$	10.8237	−	4.75609i	0.634497	−	0.278807i
$292$	−10.1569	−	2.72153i	−0.594387	−	0.159266i
$293$	1.88818	+	14.3421i	0.110309	+	0.837877i	0.953739	+	0.300637i	$0.0971994\pi$
$293$	1.88818	+	14.3421i	0.110309	+	0.837877i	−0.843430	+	0.537239i	$0.819467\pi$
$294$	0.0123350	−	0.0503002i	0.000719393	−	0.00293357i
$295$	5.16282	+	19.2679i	0.300591	+	1.12182i
$296$	4.49639	+	4.49639i	0.261348	+	0.261348i
$297$	6.25196	+	7.15060i	0.362776	+	0.414920i
$298$	10.6249	−	4.40099i	0.615486	−	0.254943i
$299$	−0.705924	−	0.0929366i	−0.0408246	−	0.00537466i
$300$	−10.6913	−	2.62181i	−0.617263	−	0.151370i
$301$	11.0463	−	1.45427i	0.636696	−	0.0838227i
$302$	−5.51071	+	0.725499i	−0.317106	+	0.0417478i
$303$	−22.3565	+	9.82376i	−1.28435	+	0.564360i
$304$	−2.50614	−	3.26606i	−0.143737	−	0.187322i
$305$			9.09164i			0.520586i
$306$	12.0234	−	17.1347i	0.687331	−	0.979525i
$307$	−11.2477	−	11.2477i	−0.641942	−	0.641942i	0.309091	−	0.951033i	$-0.399975\pi$
$307$	−11.2477	−	11.2477i	−0.641942	−	0.641942i	−0.951033	+	0.309091i	$0.899975\pi$
$308$	4.68148	−	1.25440i	0.266752	−	0.0714760i
$309$	−6.17326	−	3.39078i	−0.351184	−	0.192895i
$310$	27.9141	−	16.1162i	1.58542	−	0.915341i
$311$	19.8661	−	2.61543i	1.12651	−	0.148307i	0.455836	−	0.890064i	$-0.349340\pi$
$311$	19.8661	−	2.61543i	1.12651	−	0.148307i	0.670669	+	0.741756i	$0.266007\pi$
$312$	−1.55316	−	0.170884i	−0.0879304	−	0.00967443i
$313$	−9.87350	−	12.8674i	−0.558083	−	0.727308i	0.426058	−	0.904696i	$-0.359902\pi$
$313$	−9.87350	−	12.8674i	−0.558083	−	0.727308i	−0.984141	+	0.177388i	$0.943235\pi$
$314$	−3.99603	+	9.64728i	−0.225509	+	0.544427i
$315$	20.5503	−	17.2087i	1.15788	−	0.969602i
$316$	5.17219	+	12.4868i	0.290959	+	0.702436i
$317$	2.00513	−	15.2305i	0.112620	−	0.855430i	−0.838130	−	0.545470i	$-0.816351\pi$
$317$	2.00513	−	15.2305i	0.112620	−	0.855430i	0.950750	−	0.309960i	$-0.100316\pi$
$318$	−22.8115	+	10.0237i	−1.27920	+	0.562100i
$319$	−1.88683	+	7.04173i	−0.105642	+	0.394261i
$320$	3.25497	+	0.872167i	0.181959	+	0.0487556i
$321$	−4.69412	−	1.15113i	−0.262000	−	0.0642498i
$322$	−1.66021	+	1.27392i	−0.0925196	+	0.0709928i
$323$	−20.3113	+	20.3113i	−1.13015	+	1.13015i
$324$	−8.14915	−	3.81987i	−0.452730	−	0.212215i
$325$	5.29706	−	2.19412i	0.293828	−	0.121708i
$326$	−1.19371	+	0.319853i	−0.0661134	+	0.0177150i
$327$	−12.8372	−	9.42246i	−0.709896	−	0.521063i
$328$	5.84119	−	2.62308i	0.322526	−	0.144835i
$329$	26.5333	−	15.3190i	1.46283	−	0.844565i
$330$	9.94178	+	3.87187i	0.547277	+	0.213139i
$331$	24.4934	+	3.22461i	1.34628	+	0.177241i	0.768969	−	0.639286i	$-0.220770\pi$
$331$	24.4934	+	3.22461i	1.34628	+	0.177241i	0.577308	+	0.816526i	$0.304103\pi$
$332$	9.91490			0.544151
$333$	−16.9123	−	8.82550i	−0.926790	−	0.483634i
$334$	−6.66657	+	16.0945i	−0.364779	+	0.880653i
$335$	−1.42517	+	10.8253i	−0.0778656	+	0.591448i
$336$	−3.58294	+	2.87267i	−0.195465	+	0.156717i
$337$	−16.1747	−	4.33399i	−0.881090	−	0.236087i	−0.210213	−	0.977656i	$-0.567416\pi$
$337$	−16.1747	−	4.33399i	−0.881090	−	0.236087i	−0.670877	+	0.741568i	$0.734082\pi$
$338$	−10.5535	+	6.09308i	−0.574036	+	0.331420i
$339$	0.688515	+	2.36659i	0.0373950	+	0.128535i
$340$	3.06899	−	23.3113i	0.166440	−	1.26423i
$341$	−16.1536	+	6.69106i	−0.874769	+	0.362341i
$342$	10.1097	+	7.09398i	0.546671	+	0.383599i
$343$	−17.0737	−	7.07218i	−0.921896	−	0.381862i
$344$	−3.63918	−	2.10108i	−0.196211	−	0.113283i
$345$	−4.60560	+	0.0981913i	−0.247957	+	0.00528644i
$346$	10.0968	+	17.4881i	0.542806	+	0.940167i
$347$	−1.94905	−	14.8045i	−0.104630	−	0.794746i	−0.960642	−	0.277790i	$-0.910398\pi$
$347$	−1.94905	−	14.8045i	−0.104630	−	0.794746i	0.856012	−	0.516957i	$-0.172935\pi$
$348$	−1.04740	−	6.82779i	−0.0561468	−	0.366008i
$349$	3.36798	+	12.5695i	0.180284	+	0.672828i	0.995591	+	0.0937998i	$0.0299014\pi$
$349$	3.36798	+	12.5695i	0.180284	+	0.672828i	−0.815307	+	0.579029i	$0.803432\pi$
$350$	6.44860	−	15.5683i	0.344692	−	0.832161i
$351$	4.59889	−	0.907610i	0.245471	−	0.0484446i
$352$	−1.68881	−	0.699527i	−0.0900138	−	0.0372849i
$353$	−4.85845	+	8.41508i	−0.258589	+	0.447890i	−0.965864	−	0.259049i	$-0.916591\pi$
$353$	−4.85845	+	8.41508i	−0.258589	+	0.447890i	0.707275	+	0.706938i	$0.249924\pi$
$354$	5.31456	+	8.76801i	0.282466	+	0.466014i
$355$	0.272722	+	2.07153i	0.0144746	+	0.109945i
$356$	−3.66376	+	4.77471i	−0.194179	+	0.253059i
$357$	23.1355	+	22.1696i	1.22446	+	1.17334i
$358$	8.05674	+	1.06069i	0.425812	+	0.0560592i
$359$	7.69659			0.406210			0.203105	−	0.979157i	$-0.434897\pi$
$359$	7.69659			0.406210			0.203105	+	0.979157i	$0.434897\pi$
$360$	−10.1002	+	0.430868i	−0.532327	+	0.0227087i
$361$	1.45105	+	1.45105i	0.0763711	+	0.0763711i
$362$	9.29029	+	1.22309i	0.488287	+	0.0642842i
$363$	11.6266	+	6.38616i	0.610241	+	0.335187i
$364$	0.619070	−	2.31040i	0.0324481	−	0.121098i
$365$	30.6868	−	17.7170i	1.60622	−	0.927351i
$366$	1.30541	+	4.48700i	0.0682348	+	0.234539i
$367$	3.57478	+	13.3413i	0.186602	+	0.696408i	0.994282	+	0.106787i	$0.0340562\pi$
$367$	3.57478	+	13.3413i	0.186602	+	0.696408i	−0.807680	+	0.589621i	$0.799277\pi$
$368$	0.789261			0.0411431
$369$	−14.3590	+	12.7601i	−0.747497	+	0.664265i
$370$	−21.4281			−1.11399
$371$	−9.87187	−	36.8423i	−0.512522	−	1.91276i
$372$	11.4625	−	11.9619i	0.594301	−	0.620194i
$373$	−8.02082	+	4.63082i	−0.415302	+	0.239775i	−0.693065	−	0.720875i	$-0.743740\pi$
$373$	−8.02082	+	4.63082i	−0.415302	+	0.239775i	0.277763	+	0.960650i	$0.410407\pi$
$374$	−3.30108	+	12.3198i	−0.170695	+	0.637041i
$375$	6.76588	−	4.10101i	0.349388	−	0.211775i
$376$	−11.4566	−	1.50829i	−0.590828	−	0.0777840i
$377$	2.54404	+	2.54404i	0.131025	+	0.131025i
$378$	7.67129	−	11.4437i	0.394569	−	0.588601i
$379$	32.7079			1.68009			0.840046	−	0.542516i	$-0.182528\pi$
$379$	32.7079			1.68009			0.840046	+	0.542516i	$0.182528\pi$
$380$	13.7540	+	1.81075i	0.705567	+	0.0928897i
$381$	5.17506	−	21.1030i	0.265126	−	1.08114i
$382$	−11.8112	+	15.3926i	−0.604313	+	0.787555i
$383$	−1.24318	−	9.44290i	−0.0635236	−	0.482509i	−0.993406	−	0.114652i	$-0.963425\pi$
$383$	−1.24318	−	9.44290i	−0.0635236	−	0.482509i	0.929882	−	0.367858i	$-0.119909\pi$
$384$	1.73166	−	0.0369189i	0.0883683	−	0.00188401i
$385$	−8.16607	+	14.1440i	−0.416181	+	0.720847i
$386$	−3.46697	−	1.43607i	−0.176464	−	0.0730939i
$387$	12.3049	+	2.74084i	0.625494	+	0.139325i
$388$	2.61211	−	6.30618i	0.132610	−	0.320148i
$389$	−5.32547	−	19.8749i	−0.270012	−	1.00770i	−0.959111	−	0.283031i	$-0.908660\pi$
$389$	−5.32547	−	19.8749i	−0.270012	−	1.00770i	0.689099	−	0.724667i	$-0.258007\pi$
$390$	4.10806	−	3.29370i	0.208020	−	0.166783i
$391$	−0.718808	−	5.45989i	−0.0363517	−	0.276118i
$392$	−0.0149506	−	0.0258953i	−0.000755121	−	0.00130791i
$393$	14.6774	−	26.7216i	0.740376	−	1.34793i
$394$	−18.5765	−	10.7251i	−0.935869	−	0.540324i
$395$	−42.0779	−	17.4292i	−2.11717	−	0.876960i
$396$	5.46251	+	0.483411i	0.274501	+	0.0242923i
$397$	19.3072	−	7.99731i	0.969002	−	0.401374i	0.158661	−	0.987333i	$-0.449282\pi$
$397$	19.3072	−	7.99731i	0.969002	−	0.401374i	0.810340	+	0.585959i	$0.199282\pi$
$398$	−2.10280	+	15.9724i	−0.105404	+	0.800622i
$399$	−13.0804	+	13.6503i	−0.654838	+	0.683368i
$400$	−5.50404	+	3.17776i	−0.275202	+	0.158888i
$401$	4.48786	+	1.20252i	0.224113	+	0.0600509i	0.369128	−	0.929379i	$-0.379656\pi$
$401$	4.48786	+	1.20252i	0.224113	+	0.0600509i	−0.145015	+	0.989429i	$0.546323\pi$
$402$	0.850962	+	5.54723i	0.0424422	+	0.276671i
$403$	−1.12631	+	8.55514i	−0.0561053	+	0.426162i
$404$	−5.39534	+	13.0255i	−0.268428	+	0.648043i
$405$	28.5198	−	10.3158i	1.41716	−	0.512598i
$406$	10.5741			0.524786
$407$	11.5243	+	1.51720i	0.571236	+	0.0752047i
$408$	−1.83248	−	11.9455i	−0.0907211	−	0.591391i
$409$	29.4947	−	17.0288i	1.45842	−	0.842018i	0.459484	−	0.888186i	$-0.348034\pi$
$409$	29.4947	−	17.0288i	1.45842	−	0.842018i	0.998934	+	0.0461686i	$0.0147011\pi$
$410$	−7.66812	+	20.1687i	−0.378702	+	0.996061i
$411$	18.1726	−	7.98530i	0.896388	−	0.393886i
$412$	−3.92783	+	1.05246i	−0.193510	+	0.0518509i
$413$	−14.5003	+	6.00623i	−0.713514	+	0.295547i
$414$	−2.25891	+	0.709748i	−0.111019	+	0.0348822i
$415$	−23.6253	+	23.6253i	−1.15972	+	1.15972i
$416$	−0.715707	+	0.549181i	−0.0350904	+	0.0269258i
$417$	−4.80669	−	16.5217i	−0.235384	−	0.809072i
$418$	−7.26887	−	1.94769i	−0.355532	−	0.0952645i
$419$	7.75064	−	28.9258i	0.378644	−	1.41312i	−0.469304	−	0.883037i	$-0.655495\pi$
$419$	7.75064	−	28.9258i	0.378644	−	1.41312i	0.847947	−	0.530081i	$-0.177838\pi$
$420$	1.69244	−	15.3825i	0.0825824	−	0.750588i
$421$	1.81181	−	13.7621i	0.0883023	−	0.670722i	−0.888853	−	0.458193i	$-0.848497\pi$
$421$	1.81181	−	13.7621i	0.0883023	−	0.670722i	0.977155	−	0.212529i	$-0.0681699\pi$
$422$	−1.12707	−	2.72098i	−0.0548649	−	0.132455i
$423$	34.1457	−	5.98561i	1.66022	−	0.291030i
$424$	−5.50514	+	13.2906i	−0.267353	+	0.645448i
$425$	26.9956	+	35.1814i	1.30948	+	1.70655i
$426$	0.432034	+	0.983205i	0.0209321	+	0.0476364i
$427$	−7.09221	+	0.933708i	−0.343216	+	0.0451853i
$428$	−2.41660	+	1.39523i	−0.116811	+	0.0674407i
$429$	−2.44257	+	1.48052i	−0.117928	+	0.0714801i
$430$	13.6779	−	3.66498i	0.659607	−	0.176741i
$431$	−18.9281	−	18.9281i	−0.911737	−	0.911737i	0.0846723	−	0.996409i	$-0.473016\pi$
$431$	−18.9281	−	18.9281i	−0.911737	−	0.911737i	−0.996409	+	0.0846723i	$0.973016\pi$
$432$	−4.92289	+	1.66287i	−0.236853	+	0.0800048i
$433$		−	5.13068i		−	0.246565i	−0.992372	−	0.123282i	$-0.960658\pi$
$433$		−	5.13068i		−	0.246565i	0.992372	−	0.123282i	$-0.0393421\pi$
$434$	15.4387	+	20.1202i	0.741083	+	0.965799i
$435$	18.7651	+	13.7735i	0.899716	+	0.660391i
$436$	−9.11510	+	1.20003i	−0.436534	+	0.0574708i
$437$	3.22142	−	0.424108i	0.154101	−	0.0202878i
$438$	12.6010	−	13.1500i	0.602098	−	0.628331i
$439$	−37.7615	−	4.97140i	−1.80226	−	0.237272i	−0.846700	−	0.532071i	$-0.821414\pi$
$439$	−37.7615	−	4.97140i	−1.80226	−	0.237272i	−0.955559	+	0.294799i	$0.904747\pi$
$440$	5.69094	−	2.35726i	0.271305	−	0.112378i
$441$	0.0660760	+	0.0606691i	0.00314648	+	0.00288901i
$442$	4.45091	+	4.45091i	0.211708	+	0.211708i
$443$	−3.76560	−	14.0534i	−0.178909	−	0.667698i	−0.995853	−	0.0909804i	$-0.971000\pi$
$443$	−3.76560	−	14.0534i	−0.178909	−	0.667698i	0.816944	−	0.576718i	$-0.195667\pi$
$444$	−10.5754	+	3.07672i	−0.501887	+	0.146014i
$445$	−2.64717	−	20.1072i	−0.125488	−	0.953175i
$446$	13.2611	+	3.55331i	0.627933	+	0.168254i
$447$	−2.17844	+	19.7997i	−0.103037	+	0.936495i
$448$	−0.346077	+	2.62871i	−0.0163506	+	0.124195i
$449$	2.73035	+	2.73035i	0.128853	+	0.128853i	0.768592	−	0.639739i	$-0.220958\pi$
$449$	2.73035	+	2.73035i	0.128853	+	0.128853i	−0.639739	+	0.768592i	$0.720958\pi$
$450$	12.8952	−	14.0445i	0.607887	−	0.662062i
$451$	5.55203	−	10.3040i	0.261435	−	0.485197i
$452$	1.23236	+	0.711501i	0.0579651	+	0.0334662i
$453$	3.49375	−	8.97088i	0.164151	−	0.421489i
$454$	−4.74888	+	6.18887i	−0.222876	+	0.290458i
$455$	4.03011	+	6.98035i	0.188934	+	0.327244i
$456$	7.04803	−	1.08119i	0.330054	−	0.0506313i
$457$	−13.2501	−	17.2679i	−0.619814	−	0.807757i	0.372948	−	0.927852i	$-0.378347\pi$
$457$	−13.2501	−	17.2679i	−0.619814	−	0.807757i	−0.992762	+	0.120095i	$0.961680\pi$
$458$	−2.05152	+	0.849768i	−0.0958613	+	0.0397071i
$459$	15.9867	+	32.5408i	0.746196	+	1.51887i
$460$	−1.88065	+	1.88065i	−0.0876860	+	0.0876860i
$461$	21.1162	+	12.1914i	0.983479	+	0.567812i	0.903319	−	0.428970i	$-0.141124\pi$
$461$	21.1162	+	12.1914i	0.983479	+	0.567812i	0.0801600	+	0.996782i	$0.474457\pi$
$462$	−1.99935	+	8.15303i	−0.0930184	+	0.379313i
$463$	22.4202	+	17.2036i	1.04195	+	0.799519i	0.980088	−	0.198565i	$-0.0636282\pi$
$463$	22.4202	+	17.2036i	1.04195	+	0.799519i	0.0618659	+	0.998084i	$0.480295\pi$
$464$	−3.16401	−	2.42783i	−0.146885	−	0.112709i
$465$	1.18999	+	55.8156i	0.0551844	+	2.58839i
$466$	−3.82188	+	2.93263i	−0.177045	+	0.135851i
$467$			14.2002i			0.657106i	0.944485	+	0.328553i	$0.106561\pi$
$467$			14.2002i			0.657106i	−0.944485	+	0.328553i	$0.893439\pi$
$468$	1.55454	−	2.21539i	0.0718584	−	0.102406i
$469$	−8.59095			−0.396693
$470$	30.8928	−	23.7048i	1.42498	−	1.09342i
$471$	−11.3136	−	14.1109i	−0.521303	−	0.650195i
$472$	5.71783	+	1.53209i	0.263184	+	0.0705201i
$473$	−7.61563	+	1.00262i	−0.350167	+	0.0461004i
$474$	−23.2693	−	2.56017i	−1.06879	−	0.117593i
$475$	−20.7575	+	15.9278i	−0.952421	+	0.730819i
$476$	18.4999			0.847941
$477$	3.80435	−	42.9888i	0.174189	−	1.96832i
$478$	−18.9754	−	7.85988i	−0.867916	−	0.359503i
$479$	22.9480	+	3.02116i	1.04852	+	0.138040i	0.635045	−	0.772475i	$-0.280982\pi$
$479$	22.9480	+	3.02116i	1.04852	+	0.138040i	0.413475	+	0.910515i	$0.364315\pi$
$480$	−4.03823	+	4.21417i	−0.184319	+	0.192350i
$481$	3.49217	−	4.55108i	0.159229	−	0.207511i
$482$	−5.42509	−	9.39653i	−0.247106	−	0.428000i
$483$	−0.549590	−	3.58265i	−0.0250072	−	0.163016i
$484$	7.39763	−	1.98219i	0.336256	−	0.0900995i
$485$	8.80226	+	21.2505i	0.399690	+	0.964937i
$486$	12.5942	−	9.18616i	0.571286	−	0.416693i
$487$	−26.7694	−	26.7694i	−1.21304	−	1.21304i	−0.970023	−	0.243014i	$-0.921864\pi$
$487$	−26.7694	−	26.7694i	−1.21304	−	1.21304i	−0.243014	−	0.970023i	$-0.578136\pi$
$488$	2.33652	+	1.34899i	0.105769	+	0.0610659i
$489$	0.509806	−	2.07890i	0.0230542	−	0.0940112i
$490$	0.0973278	+	0.0260789i	0.00439682	+	0.00117813i
$491$	11.8270	+	20.4849i	0.533744	+	0.924471i	0.999223	+	0.0394126i	$0.0125487\pi$
$491$	11.8270	+	20.4849i	0.533744	+	0.924471i	−0.465479	+	0.885059i	$0.654118\pi$
$492$	−0.888563	+	11.0549i	−0.0400595	+	0.498393i
$493$	−13.9135	+	24.0988i	−0.626631	+	1.08536i
$494$	−2.62610	+	2.62610i	−0.118154	+	0.118154i
$495$	−14.1680	+	11.8642i	−0.636803	+	0.533257i
$496$		−	9.56511i		−	0.429486i
$497$	−1.58795	+	0.425490i	−0.0712294	+	0.0190859i
$498$	−8.26760	+	15.0520i	−0.370480	+	0.674496i
$499$	−13.6034	+	17.7283i	−0.608971	+	0.793627i	−0.991471	−	0.130329i	$-0.958397\pi$
$499$	−13.6034	+	17.7283i	−0.608971	+	0.793627i	0.382500	+	0.923956i	$0.375063\pi$
$500$	1.18224	−	4.41219i	0.0528715	−	0.197319i
$501$	−18.8744	−	23.5412i	−0.843248	−	1.05174i
$502$	−3.99765	+	6.92414i	−0.178424	+	0.309039i
$503$	−16.9072	−	40.8175i	−0.753853	−	1.81996i	−0.536575	−	0.843853i	$-0.680282\pi$
$503$	−16.9072	−	40.8175i	−0.753853	−	1.81996i	−0.217278	−	0.976110i	$-0.569718\pi$
$504$	−1.37340	−	7.83472i	−0.0611760	−	0.348986i
$505$	−18.1812	−	43.8933i	−0.809052	−	1.95322i
$506$	1.14460	−	0.878279i	0.0508835	−	0.0390443i
$507$	−0.449900	−	21.1023i	−0.0199808	−	0.937184i
$508$	−6.27242	−	10.8641i	−0.278293	−	0.482018i
$509$	−4.42376	−	33.6018i	−0.196080	−	1.48937i	−0.752567	−	0.658516i	$-0.771185\pi$
$509$	−4.42376	−	33.6018i	−0.196080	−	1.48937i	0.556487	−	0.830856i	$-0.312149\pi$
$510$	32.8303	+	24.0974i	1.45375	+	1.06705i
$511$	16.9722	+	22.1186i	0.750807	+	0.978470i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−19.1996	+	9.43241i	−0.847681	+	0.416451i
$514$	−22.1257	−	9.16478i	−0.975925	−	0.404241i
$515$	6.85145	−	11.8671i	0.301911	−	0.522925i
$516$	6.22424	−	3.77270i	0.274007	−	0.166084i
$517$	−18.2929	+	10.5614i	−0.804520	+	0.464490i
$518$	−2.20065	−	16.7156i	−0.0966912	−	0.734442i
$519$	−34.9683	+	0.745523i	−1.53494	+	0.0327248i
$520$	0.396798	−	3.01398i	0.0174008	−	0.132172i
$521$	7.16805	−	2.96910i	0.314038	−	0.130079i	−0.220097	−	0.975478i	$-0.570637\pi$
$521$	7.16805	−	2.96910i	0.314038	−	0.130079i	0.534135	+	0.845399i	$0.320637\pi$
$522$	11.2388	+	4.10331i	0.491908	+	0.179597i
$523$			13.8896i			0.607350i	0.952776	+	0.303675i	$0.0982138\pi$
$523$			13.8896i			0.607350i	−0.952776	+	0.303675i	$0.901786\pi$
$524$	−4.55568	−	17.0020i	−0.199016	−	0.742738i
$525$	18.2573	+	22.7715i	0.796815	+	0.993828i
$526$	17.1361	+	13.1490i	0.747168	+	0.573322i
$527$	−66.1688	+	8.71129i	−2.88236	+	0.379470i
$528$	2.47019	−	1.98051i	0.107501	−	0.0861905i
$529$	11.1885	−	19.3791i	0.486458	−	0.842570i
$530$	−18.5512	−	44.7865i	−0.805812	−	1.94540i
$531$	−17.7425	+	0.756882i	−0.769957	+	0.0328459i
$532$			10.9152i			0.473235i
$533$	−3.03392	−	4.91555i	−0.131414	−	0.212916i
$534$	−4.19353	−	9.54345i	−0.181472	−	0.412985i
$535$	2.43374	−	9.08284i	0.105220	−	0.392685i
$536$	2.57059	+	1.97248i	0.111033	+	0.0851984i
$537$	−8.32841	+	11.3466i	−0.359397	+	0.489643i
$538$	5.94425	+	22.1842i	0.256275	+	0.956431i
$539$	−0.0504975	−	0.0209168i	−0.00217508	−	0.000900948i
$540$	7.76800	−	15.6926i	0.334282	−	0.675301i
$541$	12.6663	−	12.6663i	0.544566	−	0.544566i	−0.380298	−	0.924864i	$-0.624179\pi$
$541$	12.6663	−	12.6663i	0.544566	−	0.544566i	0.924864	+	0.380298i	$0.124179\pi$
$542$	12.4050	−	3.32391i	0.532841	−	0.142774i
$543$	−9.60356	+	13.0839i	−0.412128	+	0.561483i
$544$	−5.53556	−	4.24758i	−0.237335	−	0.182114i
$545$	18.8601	−	24.5789i	0.807877	−	1.05285i
$546$	2.99125	+	2.86636i	0.128013	+	0.122669i
$547$	−7.08948	−	9.23920i	−0.303124	−	0.395040i	0.616810	−	0.787112i	$-0.288425\pi$
$547$	−7.08948	−	9.23920i	−0.303124	−	0.395040i	−0.919934	+	0.392073i	$0.871758\pi$
$548$	4.38563	−	10.5878i	0.187345	−	0.452290i
$549$	−7.90033	−	1.75975i	−0.337178	−	0.0751042i
$550$	−4.44586	+	10.7333i	−0.189572	+	0.457668i
$551$	−14.2187	−	8.20916i	−0.605736	−	0.349722i
$552$	−0.658130	+	1.19819i	−0.0280119	+	0.0509984i
$553$	9.27483	−	34.6141i	0.394406	−	1.47194i
$554$	4.55364	−	16.9944i	0.193466	−	0.722024i
$555$	17.8679	−	32.5303i	0.758451	−	1.38084i
$556$	−8.60337	−	4.96716i	−0.364864	−	0.210654i
$557$	−12.9176	+	31.1859i	−0.547338	+	1.32139i	0.372114	+	0.928187i	$0.378633\pi$
$557$	−12.9176	+	31.1859i	−0.547338	+	1.32139i	−0.919452	+	0.393203i	$0.871367\pi$
$558$	8.60149	+	27.3758i	0.364130	+	1.15891i
$559$	−1.45071	+	3.50232i	−0.0613585	+	0.148133i
$560$	−5.43908	−	7.08834i	−0.229843	−	0.299537i
$561$	−15.9503	−	15.2844i	−0.673421	−	0.645306i
$562$	6.92575	−	9.02582i	0.292145	−	0.380731i
$563$	10.4648	+	8.02989i	0.441037	+	0.338420i	0.805291	−	0.592880i	$-0.202009\pi$
$563$	10.4648	+	8.02989i	0.441037	+	0.338420i	−0.364254	+	0.931300i	$0.618676\pi$
$564$	11.8429	−	16.1348i	0.498676	−	0.679396i
$565$	−4.63183	+	1.24110i	−0.194863	+	0.0522133i
$566$	−9.29438	+	9.29438i	−0.390672	+	0.390672i
$567$	10.9762	+	21.1883i	0.460956	+	0.889827i
$568$	0.572841	+	0.237279i	0.0240359	+	0.00995599i
$569$	5.99327	+	22.3672i	0.251251	+	0.937681i	0.970138	+	0.242554i	$0.0779851\pi$
$569$	5.99327	+	22.3672i	0.251251	+	0.937681i	−0.718887	+	0.695127i	$0.755348\pi$
$570$	−14.2178	+	19.3704i	−0.595519	+	0.811335i
$571$	−3.84519	−	2.95052i	−0.160916	−	0.123475i	0.525165	−	0.851001i	$-0.324004\pi$
$571$	−3.84519	−	2.95052i	−0.160916	−	0.123475i	−0.686081	+	0.727525i	$0.740670\pi$
$572$	−0.426805	+	1.59286i	−0.0178456	+	0.0666008i
$573$	−13.5190	−	30.7660i	−0.564765	−	1.28527i
$574$	−16.5207	−	3.91044i	−0.689562	−	0.163219i
$575$		−	5.01617i		−	0.209189i
$576$	−1.38791	+	2.65965i	−0.0578294	+	0.110819i
$577$	−9.09835	−	21.9654i	−0.378769	−	0.914430i	−0.992197	−	0.124679i	$-0.960210\pi$
$577$	−9.09835	−	21.9654i	−0.378769	−	0.914430i	0.613428	−	0.789751i	$-0.289790\pi$
$578$	−15.8422	+	27.4395i	−0.658948	+	1.14133i
$579$	5.07107	−	4.06580i	0.210747	−	0.168969i
$580$	13.3242	−	1.75417i	0.553259	−	0.0728380i
$581$	−20.8559	−	16.0033i	−0.865250	−	0.663929i
$582$	7.39541	+	9.22393i	0.306550	+	0.382344i
$583$	6.80596	+	25.4002i	0.281874	+	1.05197i
$584$		−	10.5152i		−	0.435121i
$585$	1.57469	+	8.98300i	0.0651053	+	0.371401i
$586$	−13.3647	+	5.53586i	−0.552092	+	0.228684i
$587$	−4.58382	+	34.8175i	−0.189194	+	1.43707i	0.588534	+	0.808473i	$0.299705\pi$
$587$	−4.58382	+	34.8175i	−0.189194	+	1.43707i	−0.777728	+	0.628601i	$0.783628\pi$
$588$	0.0517788	−	0.00110392i	0.00213532	−	4.55250e-5i
$589$	−5.13980	−	39.0406i	−0.211782	−	1.60864i
$590$	−17.2751	+	9.97381i	−0.711206	+	0.410615i
$591$	31.7721	−	19.2581i	1.30693	−	0.792171i
$592$	−3.17943	+	5.50694i	−0.130674	+	0.226334i
$593$	1.74742	+	0.723805i	0.0717580	+	0.0297231i	0.418274	−	0.908321i	$-0.362635\pi$
$593$	1.74742	+	0.723805i	0.0717580	+	0.0297231i	−0.346516	+	0.938044i	$0.612635\pi$
$594$	−5.28882	+	7.88964i	−0.217003	+	0.323716i
$595$	−44.0817	+	44.0817i	−1.80717	+	1.80717i
$596$	7.00097	+	9.12384i	0.286771	+	0.373727i
$597$	−22.4945	−	16.5109i	−0.920639	−	0.675748i
$598$	−0.0929366	−	0.705924i	−0.00380046	−	0.0288674i
$599$	16.9266	+	29.3177i	0.691600	+	1.19789i	0.971313	+	0.237803i	$0.0764274\pi$
$599$	16.9266	+	29.3177i	0.691600	+	1.19789i	−0.279713	+	0.960084i	$0.590239\pi$
$600$	−0.234639	−	11.0056i	−0.00957910	−	0.449301i
$601$	19.3315	−	14.8336i	0.788549	−	0.605075i	−0.133988	−	0.990983i	$-0.542778\pi$
$601$	19.3315	−	14.8336i	0.788549	−	0.605075i	0.922537	+	0.385908i	$0.126112\pi$
$602$	4.26370	+	10.2935i	0.173775	+	0.419531i
$603$	−9.13094	−	3.33373i	−0.371841	−	0.135760i
$604$	−2.12706	−	5.13517i	−0.0865487	−	0.208947i
$605$	−12.9039	+	22.3503i	−0.524620	+	0.908668i
$606$	−15.2753	−	19.0522i	−0.620517	−	0.773941i
$607$	−2.21005	+	8.24802i	−0.0897032	+	0.334777i	−0.996163	−	0.0875148i	$-0.972107\pi$
$607$	−2.21005	+	8.24802i	−0.0897032	+	0.334777i	0.906460	+	0.422292i	$0.138774\pi$
$608$	2.50614	−	3.26606i	0.101637	−	0.132456i
$609$	−8.81731	+	16.0528i	−0.357296	+	0.650492i
$610$	−8.78185	+	2.35309i	−0.355567	+	0.0952738i
$611$			10.4245i			0.421730i
$612$	19.6627	+	7.17891i	0.794818	+	0.290190i
$613$	−20.5922	+	20.5922i	−0.831709	+	0.831709i	−0.987751	−	0.156041i	$-0.950127\pi$
$613$	−20.5922	+	20.5922i	−0.831709	+	0.831709i	0.156041	+	0.987751i	$0.450127\pi$
$614$	7.95334	−	13.7756i	0.320971	−	0.555938i
$615$	−24.2244	−	28.4589i	−0.976821	−	1.14757i
$616$	2.42331	+	4.19730i	0.0976381	+	0.169114i
$617$	−10.8273	−	2.90118i	−0.435892	−	0.116797i	0.0341985	−	0.999415i	$-0.489112\pi$
$617$	−10.8273	−	2.90118i	−0.435892	−	0.116797i	−0.470091	+	0.882618i	$0.655779\pi$
$618$	1.67749	−	6.84051i	0.0674784	−	0.275166i
$619$	20.0163	+	11.5564i	0.804522	+	0.464491i	0.845050	−	0.534687i	$-0.179571\pi$
$619$	20.0163	+	11.5564i	0.804522	+	0.464491i	−0.0405279	+	0.999178i	$0.512904\pi$
$620$	22.7918	+	22.7918i	0.915341	+	0.915341i
$621$	0.806120	−	4.02111i	0.0323485	−	0.161362i
$622$	7.66804	+	18.5123i	0.307461	+	0.742275i
$623$	15.4134	−	4.13001i	0.617525	−	0.165465i
$624$	−0.236926	−	1.54447i	−0.00948462	−	0.0618281i
$625$	−8.19247	−	14.1898i	−0.327699	−	0.567591i
$626$	9.87350	−	12.8674i	0.394624	−	0.514284i
$627$	9.01801	−	9.41091i	0.360144	−	0.375836i
$628$	−10.3528	−	1.36297i	−0.413122	−	0.0543885i
$629$	40.9911	+	16.9791i	1.63442	+	0.677000i
$630$	21.9412	+	15.3961i	0.874157	+	0.613394i
$631$	27.5775			1.09784			0.548921	−	0.835874i	$-0.315039\pi$
$631$	27.5775			1.09784			0.548921	+	0.835874i	$0.315039\pi$
$632$	−10.7226	+	8.22777i	−0.426524	+	0.327283i
$633$	5.07059	+	0.557885i	0.201538	+	0.0221739i
$634$	15.2305	−	2.00513i	0.604880	−	0.0796340i
$635$	40.8331	+	10.9412i	1.62041	+	0.434188i
$636$	−15.5862	−	19.4399i	−0.618032	−	0.770841i
$637$	−0.0214006	+	0.0164212i	−0.000847921	+	0.000650632i
$638$	−7.29013			−0.288619
$639$	−1.85288	−	0.163972i	−0.0732986	−	0.00648664i
$640$			3.36980i			0.133203i
$641$	−37.7889	+	28.9964i	−1.49257	+	1.14529i	−0.539724	+	0.841842i	$0.681471\pi$
$641$	−37.7889	+	28.9964i	−1.49257	+	1.14529i	−0.952848	+	0.303448i	$0.901862\pi$
$642$	−0.103020	−	4.83210i	−0.00406589	−	0.190708i
$643$	−1.71725	−	1.31769i	−0.0677217	−	0.0519647i	0.574346	−	0.818613i	$-0.305256\pi$
$643$	−1.71725	−	1.31769i	−0.0677217	−	0.0519647i	−0.642068	+	0.766648i	$0.721923\pi$
$644$	−1.66021	−	1.27392i	−0.0654213	−	0.0501995i
$645$	−5.84152	+	23.8208i	−0.230010	+	0.937941i
$646$	−24.8762	−	14.3623i	−0.978740	−	0.565076i
$647$	6.90273	−	6.90273i	0.271374	−	0.271374i	−0.558279	−	0.829653i	$-0.688538\pi$
$647$	6.90273	−	6.90273i	0.271374	−	0.271374i	0.829653	+	0.558279i	$0.188538\pi$
$648$	1.58055	−	8.86013i	0.0620899	−	0.348059i
$649$	9.99695	−	4.14087i	0.392415	−	0.162543i
$650$	3.49033	+	4.54869i	0.136902	+	0.178414i
$651$	−43.4185	+	6.66053i	−1.70170	+	0.261047i
$652$	−0.617909	−	1.07025i	−0.0241992	−	0.0419142i
$653$	−21.9354	+	28.5868i	−0.858398	+	1.11869i	0.133424	+	0.991059i	$0.457403\pi$
$653$	−21.9354	+	28.5868i	−0.858398	+	1.11869i	−0.991822	+	0.127627i	$0.959264\pi$
$654$	5.77890	−	14.8384i	0.225973	−	0.580229i
$655$	51.3679	+	29.6573i	2.00711	+	1.15880i
$656$	4.04551	+	4.96325i	0.157951	+	0.193782i
$657$	9.45585	+	30.0950i	0.368908	+	1.17412i
$658$	21.6644	+	21.6644i	0.844565	+	0.844565i
$659$	−4.41933	+	33.5681i	−0.172152	+	1.30763i	0.659236	+	0.751936i	$0.270880\pi$
$659$	−4.41933	+	33.5681i	−0.172152	+	1.30763i	−0.831388	+	0.555692i	$0.812453\pi$
$660$	−1.16682	+	10.6051i	−0.0454183	+	0.412804i
$661$	−17.3792	−	4.65674i	−0.675972	−	0.181126i	−0.0955288	−	0.995427i	$-0.530454\pi$
$661$	−17.3792	−	4.65674i	−0.675972	−	0.181126i	−0.580444	+	0.814300i	$0.697121\pi$
$662$	3.22461	+	24.4934i	0.125328	+	0.951962i
$663$	−10.4684	+	3.04559i	−0.406560	+	0.118281i
$664$	2.56616	+	9.57705i	0.0995865	+	0.371662i
$665$	−26.0089	−	26.0089i	−1.00858	−	1.00858i
$666$	4.14755	−	18.6203i	0.160714	−	0.721520i
$667$	2.90808	−	1.20457i	0.112601	−	0.0466410i
$668$	−17.2716	−	2.27384i	−0.668257	−	0.0879777i
$669$	−16.4522	+	17.1690i	−0.636079	+	0.663793i
$670$	−10.8253	+	1.42517i	−0.418217	+	0.0550593i
$671$	4.88959	−	0.643726i	0.188760	−	0.0248508i
$672$	−3.70212	−	2.71735i	−0.142812	−	0.104824i
$673$	−1.44984	−	1.88947i	−0.0558873	−	0.0728337i	0.764573	−	0.644537i	$-0.222950\pi$
$673$	−1.44984	−	1.88947i	−0.0558873	−	0.0728337i	−0.820461	+	0.571703i	$0.806283\pi$
$674$		−	16.7452i		−	0.645003i
$675$	10.5684	+	31.2876i	0.406778	+	1.20426i
$676$	−8.61692	−	8.61692i	−0.331420	−	0.331420i
$677$	−22.8642	+	6.12645i	−0.878743	+	0.235459i	−0.669865	−	0.742483i	$-0.733648\pi$
$677$	−22.8642	+	6.12645i	−0.878743	+	0.235459i	−0.208878	+	0.977942i	$0.566981\pi$
$678$	−2.10775	+	1.27757i	−0.0809476	+	0.0490649i
$679$	−15.6731	+	9.04890i	−0.601480	+	0.347265i
$680$	23.3113	−	3.06899i	0.893948	−	0.117691i
$681$	−5.43555	−	12.3700i	−0.208291	−	0.474019i
$682$	−10.6439	−	13.8714i	−0.407577	−	0.531165i
$683$	−6.87187	+	16.5901i	−0.262945	+	0.634804i	−0.999118	−	0.0419884i	$-0.986631\pi$
$683$	−6.87187	+	16.5901i	−0.262945	+	0.634804i	0.736173	+	0.676793i	$0.236631\pi$
$684$	−4.23567	+	11.6013i	−0.161955	+	0.443587i
$685$	14.7787	+	35.6789i	0.564664	+	1.36322i
$686$	2.41219	−	18.3224i	0.0920978	−	0.699552i
$687$	0.420625	−	3.82304i	0.0160478	−	0.145858i
$688$	1.08760	−	4.05897i	0.0414643	−	0.154747i
$689$	12.5355	+	3.35887i	0.477564	+	0.127963i
$690$	−1.28686	−	4.42325i	−0.0489900	−	0.168390i
$691$	−27.4471	+	21.0609i	−1.04414	+	0.801194i	−0.980449	−	0.196776i	$-0.936953\pi$
$691$	−27.4471	+	21.0609i	−1.04414	+	0.801194i	−0.0636881	+	0.997970i	$0.520286\pi$
$692$	−14.2790	+	14.2790i	−0.542806	+	0.542806i
$693$	−10.7101	−	9.83371i	−0.406843	−	0.373552i
$694$	13.7956	−	5.71432i	0.523673	−	0.216913i
$695$	32.3359	−	8.66438i	1.22657	−	0.328659i
$696$	6.32405	−	2.77888i	0.239713	−	0.105333i
$697$	30.6500	−	32.5059i	1.16095	−	1.23125i
$698$	−11.2695	+	6.50644i	−0.426556	+	0.246272i
$699$	−1.26518	−	8.24745i	−0.0478537	−	0.311947i
$700$	16.7068	+	2.19950i	0.631459	+	0.0831332i
$701$	30.0325			1.13431			0.567156	−	0.823611i	$-0.308044\pi$
$701$	30.0325			1.13431			0.567156	+	0.823611i	$0.308044\pi$
$702$	2.06697	+	4.20728i	0.0780126	+	0.158794i
$703$	−10.0179	+	24.1854i	−0.377833	+	0.912169i
$704$	0.238596	−	1.81231i	0.00899241	−	0.0683042i
$705$	10.2267	+	66.6653i	0.385158	+	2.51076i
$706$	−9.38580	−	2.51492i	−0.353239	−	0.0946502i
$707$	32.3731	−	18.6906i	1.21752	−	0.702933i
$708$	−7.09374	+	7.40280i	−0.266599	+	0.278214i
$709$	4.01823	−	30.5215i	0.150908	−	1.14626i	−0.733550	−	0.679636i	$-0.762138\pi$
$709$	4.01823	−	30.5215i	0.150908	−	1.14626i	0.884457	−	0.466621i	$-0.154529\pi$
$710$	−1.93036	+	0.799580i	−0.0724450	+	0.0300077i
$711$	23.2899	−	33.1907i	0.873438	−	1.24475i
$712$	−5.56027	−	2.30314i	−0.208380	−	0.0863138i
$713$	6.53795	+	3.77469i	0.244848	+	0.141363i
$714$	−15.4263	+	28.0850i	−0.577313	+	1.05106i
$715$	−2.77848	−	4.81247i	−0.103909	−	0.179976i
$716$	1.06069	+	8.05674i	0.0396398	+	0.301094i
$717$	27.7550	−	22.2530i	1.03653	−	0.831052i
$718$	1.99202	+	7.43433i	0.0743417	+	0.277447i
$719$	−14.9167	+	36.0121i	−0.556299	+	1.34303i	0.356377	+	0.934342i	$0.384012\pi$
$719$	−14.9167	+	36.0121i	−0.556299	+	1.34303i	−0.912676	+	0.408683i	$0.865988\pi$
$720$	−3.03031	−	9.64453i	−0.112933	−	0.359430i
$721$	9.96090	+	4.12594i	0.370963	+	0.153658i
$722$	−1.02605	+	1.77717i	−0.0381856	+	0.0661393i
$723$	18.7888	−	0.400577i	0.698762	−	0.0148976i
$724$	1.22309	+	9.29029i	0.0454558	+	0.345271i
$725$	−15.4301	+	20.1089i	−0.573060	+	0.746826i
$726$	−3.15936	+	12.8833i	−0.117255	+	0.478146i
$727$	−6.55838	−	0.863427i	−0.243237	−	0.0320227i	0.00792203	−	0.999969i	$-0.497478\pi$
$727$	−6.55838	−	0.863427i	−0.243237	−	0.0320227i	−0.251159	+	0.967946i	$0.580812\pi$
$728$	2.39190			0.0886498
$729$	3.44391	+	26.7795i	0.127552	+	0.991832i
$730$	25.0556	+	25.0556i	0.927351	+	0.927351i
$731$	−29.0694	−	3.82706i	−1.07517	−	0.141549i
$732$	−3.99625	+	2.42225i	−0.147706	+	0.0895289i
$733$	−3.90401	+	14.5700i	−0.144198	+	0.538154i	0.855592	+	0.517651i	$0.173193\pi$
$733$	−3.90401	+	14.5700i	−0.144198	+	0.538154i	−0.999790	+	0.0205029i	$0.993473\pi$
$734$	−11.9614	+	6.90594i	−0.441505	+	0.254903i
$735$	−0.120748	+	0.126009i	−0.00445387	+	0.00464792i
$736$	0.204276	+	0.762367i	0.00752970	+	0.0281012i
$737$	5.92286			0.218171
$738$	−16.0417	−	10.5671i	−0.590503	−	0.388981i
$739$	3.29887			0.121351			0.0606755	−	0.998158i	$-0.480675\pi$
$739$	3.29887			0.121351			0.0606755	+	0.998158i	$0.480675\pi$
$740$	−5.54599	−	20.6979i	−0.203875	−	0.760871i
$741$	−1.79694	−	6.17653i	−0.0660124	−	0.226900i
$742$	33.0319	−	19.0710i	1.21264	−	0.700118i
$743$	5.78836	−	21.6025i	0.212354	−	0.792517i	−0.774727	−	0.632296i	$-0.782113\pi$
$743$	5.78836	−	21.6025i	0.212354	−	0.792517i	0.987081	−	0.160221i	$-0.0512208\pi$
$744$	14.5210	+	7.97593i	0.532365	+	0.292412i
$745$	−38.4223	−	5.05839i	−1.40768	−	0.185325i
$746$	−6.54897	−	6.54897i	−0.239775	−	0.239775i
$747$	−15.9567	−	25.1024i	−0.583826	−	0.918448i
$748$	−12.7544			−0.466347
$749$	7.33529	+	0.965710i	0.268026	+	0.0352863i
$750$	5.71241	+	5.47392i	0.208588	+	0.199879i
$751$	9.93829	−	12.9518i	0.362653	−	0.472619i	−0.576016	−	0.817439i	$-0.695393\pi$
$751$	9.93829	−	12.9518i	0.362653	−	0.472619i	0.938669	+	0.344820i	$0.112060\pi$
$752$	−1.50829	−	11.4566i	−0.0550016	−	0.417779i
$753$	−7.17820	−	11.8426i	−0.261588	−	0.431570i
$754$	−1.79891	+	3.11580i	−0.0655124	+	0.113471i
$755$	17.3045	+	7.16774i	0.629774	+	0.260861i
$756$	13.0393	+	4.44805i	0.474233	+	0.161774i
$757$	−15.2727	+	36.8716i	−0.555096	+	1.34012i	0.358512	+	0.933525i	$0.383284\pi$
$757$	−15.2727	+	36.8716i	−0.555096	+	1.34012i	−0.913608	+	0.406596i	$0.866716\pi$
$758$	8.46542	+	31.5934i	0.307478	+	1.14752i
$759$	0.378904	+	2.46999i	0.0137533	+	0.0896550i
$760$	1.81075	+	13.7540i	0.0656829	+	0.498911i
$761$	18.2613	+	31.6295i	0.661971	+	1.14657i	0.980097	+	0.198519i	$0.0636131\pi$
$761$	18.2613	+	31.6295i	0.661971	+	1.14657i	−0.318126	+	0.948048i	$0.603054\pi$
$762$	21.7234	−	0.463142i	0.786954	−	0.0167778i
$763$	21.1105	+	12.1881i	0.764251	+	0.441240i
$764$	−17.9251	−	7.42482i	−0.648507	−	0.268621i
$765$	−63.9584	+	29.7465i	−2.31242	+	1.07549i
$766$	8.79938	−	3.64482i	0.317934	−	0.131693i
$767$	0.697034	−	5.29450i	0.0251684	−	0.191173i
$768$	0.483847	+	1.66310i	0.0174593	+	0.0600119i
$769$	16.5985	−	9.58317i	0.598559	−	0.345578i	−0.169916	−	0.985459i	$-0.554350\pi$
$769$	16.5985	−	9.58317i	0.598559	−	0.345578i	0.768474	+	0.639881i	$0.221016\pi$
$770$	−15.7756	−	4.22707i	−0.568514	−	0.152333i
$771$	32.3629	−	25.9474i	1.16552	−	0.934473i
$772$	0.489816	−	3.72052i	0.0176288	−	0.133904i
$773$	14.5486	−	35.1233i	0.523275	−	1.26330i	−0.412582	−	0.910920i	$-0.635373\pi$
$773$	14.5486	−	35.1233i	0.523275	−	1.26330i	0.935858	−	0.352378i	$-0.114627\pi$
$774$	0.537295	+	12.5950i	0.0193127	+	0.452719i
$775$	−60.7913			−2.18369
$776$	6.76736	+	0.890940i	0.242934	+	0.0319829i
$777$	27.2113	+	10.5976i	0.976201	+	0.380186i
$778$	17.8194	−	10.2880i	0.638855	−	0.368843i
$779$	19.1790	+	18.0840i	0.687159	+	0.647926i
$780$	4.24471	+	3.11561i	0.151985	+	0.111557i
$781$	1.09478	−	0.293346i	0.0391744	−	0.0104967i
$782$	5.08781	−	2.10744i	0.181940	−	0.0753619i
$783$	−15.6008	+	13.6402i	−0.557529	+	0.487462i
$784$	0.0211434	−	0.0211434i	0.000755121	−	0.000755121i
$785$	27.9164	−	21.4210i	0.996379	−	0.764549i
$786$	29.6099	+	7.26119i	1.05615	+	0.258998i
$787$	35.0494	+	9.39146i	1.24938	+	0.334769i	0.822095	−	0.569350i	$-0.192805\pi$
$787$	35.0494	+	9.39146i	1.24938	+	0.334769i	0.427281	+	0.904119i	$0.359472\pi$
$788$	5.55174	−	20.7194i	0.197772	−	0.738097i
$789$	−34.2507	+	15.0502i	−1.21936	+	0.535802i
$790$	5.94479	−	45.1551i	0.211506	−	1.60655i
$791$	−1.44384	−	3.48574i	−0.0513371	−	0.123939i
$792$	0.946862	+	5.40149i	0.0336453	+	0.191934i
$793$	0.931423	−	2.24865i	0.0330758	−	0.0798520i
$794$	12.7219	+	16.5795i	0.451483	+	0.588384i
$795$	83.4603	+	9.18261i	2.96003	+	0.325674i
$796$	−15.9724	+	2.10280i	−0.566125	+	0.0745318i
$797$	−43.0610	+	24.8613i	−1.52530	+	0.880631i	−0.525747	+	0.850641i	$0.676214\pi$
$797$	−43.0610	+	24.8613i	−1.52530	+	0.880631i	−0.999550	+	0.0299902i	$0.990452\pi$
$798$	−16.5706	−	9.10172i	−0.586593	−	0.322198i
$799$	−77.8798	+	20.8678i	−2.75519	+	0.738251i
$800$	−4.49403	−	4.49403i	−0.158888	−	0.158888i
$801$	17.9849	+	1.59159i	0.635465	+	0.0562362i
$802$			4.64618i			0.164062i
$803$	−11.7012	−	15.2492i	−0.412925	−	0.538134i
$804$	−5.13797	+	2.25770i	−0.181202	+	0.0796228i
$805$	6.99145	−	0.920442i	0.246416	−	0.0324413i
$806$	−8.55514	+	1.12631i	−0.301342	+	0.0396724i
$807$	−38.6350	−	9.47439i	−1.36002	−	0.333514i
$808$	−13.9781	−	1.84025i	−0.491747	−	0.0647397i
$809$	21.6266	−	8.95802i	0.760350	−	0.314947i	0.0313933	−	0.999507i	$-0.490006\pi$
$809$	21.6266	−	8.95802i	0.760350	−	0.314947i	0.728957	+	0.684560i	$0.240006\pi$
$810$	17.3458	+	24.8781i	0.609470	+	0.874128i
$811$	−10.0815	−	10.0815i	−0.354010	−	0.354010i	0.507589	−	0.861599i	$-0.330537\pi$
$811$	−10.0815	−	10.0815i	−0.354010	−	0.354010i	−0.861599	+	0.507589i	$0.830537\pi$
$812$	2.73679	+	10.2138i	0.0960425	+	0.358435i
$813$	−5.29790	+	21.6039i	−0.185805	+	0.757684i
$814$	1.51720	+	11.5243i	0.0531777	+	0.403925i
$815$	4.02255	+	1.07784i	0.140904	+	0.0377551i
$816$	11.0642	−	4.86176i	0.387324	−	0.170196i
$817$	2.25802	−	17.1514i	0.0789982	−	0.600051i
$818$	24.0823	+	24.0823i	0.842018	+	0.842018i
$819$	−6.84574	+	2.15093i	−0.239210	+	0.0751597i
$820$	−21.4661	−	2.18680i	−0.749629	−	0.0763662i
$821$	33.2792	+	19.2137i	1.16145	+	0.670564i	0.951651	−	0.307180i	$-0.0993853\pi$
$821$	33.2792	+	19.2137i	1.16145	+	0.670564i	0.209800	+	0.977744i	$0.432719\pi$
$822$	12.4166	+	15.4866i	0.433079	+	0.540159i
$823$	7.76646	−	10.1214i	0.270722	−	0.352811i	−0.638132	−	0.769927i	$-0.720292\pi$
$823$	7.76646	−	10.1214i	0.270722	−	0.352811i	0.908853	+	0.417116i	$0.136959\pi$
$824$	−2.03319	−	3.52160i	−0.0708297	−	0.122681i
$825$	−12.5871	−	15.6993i	−0.438228	−	0.546581i
$826$	−9.55453	−	12.4517i	−0.332444	−	0.433250i
$827$	−4.00343	+	1.65828i	−0.139213	+	0.0576639i	−0.451202	−	0.892422i	$-0.649005\pi$
$827$	−4.00343	+	1.65828i	−0.139213	+	0.0576639i	0.311989	+	0.950086i	$0.399005\pi$
$828$	−1.27021	−	1.99824i	−0.0441429	−	0.0694436i
$829$	15.4015	−	15.4015i	0.534915	−	0.534915i	−0.387116	−	0.922031i	$-0.626529\pi$
$829$	15.4015	−	15.4015i	0.534915	−	0.534915i	0.922031	+	0.387116i	$0.126529\pi$
$830$	−28.9349	−	16.7056i	−1.00435	−	0.579859i
$831$	22.0025	+	21.0839i	0.763257	+	0.731391i
$832$	−0.715707	−	0.549181i	−0.0248127	−	0.0190394i
$833$	−0.165520	−	0.127008i	−0.00573494	−	0.00440057i
$834$	14.7147	−	8.91904i	0.509528	−	0.308841i
$835$	46.5729	−	35.7366i	1.61172	−	1.23672i
$836$		−	7.52528i		−	0.260267i
$837$	−48.7322	−	9.76943i	−1.68443	−	0.337681i
$838$	29.9462			1.03447
$839$	−16.7334	+	12.8400i	−0.577700	+	0.443285i	−0.855829	−	0.517259i	$-0.826952\pi$
$839$	−16.7334	+	12.8400i	−0.577700	+	0.443285i	0.278129	+	0.960544i	$0.410286\pi$
$840$	15.2964	−	2.34651i	0.527774	−	0.0809622i
$841$	12.6485	+	3.38916i	0.436156	+	0.116868i
$842$	13.7621	−	1.81181i	0.474272	−	0.0624391i
$843$	7.92718	+	18.0403i	0.273027	+	0.621342i
$844$	2.33656	−	1.79291i	0.0804278	−	0.0617144i
$845$	41.0649			1.41267
$846$	14.6192	+	31.4330i	0.502619	+	1.08069i
$847$	−18.7603	−	7.77075i	−0.644610	−	0.267006i
$848$	−14.2625	−	1.87770i	−0.489778	−	0.0644805i
$849$	−6.35980	−	21.8602i	−0.218268	−	0.750239i
$850$	−26.9956	+	35.1814i	−0.925942	+	1.20671i
$851$	−2.50940	−	4.34641i	−0.0860211	−	0.148993i
$852$	−0.837884	+	0.671785i	−0.0287054	+	0.0230150i
$853$	15.5682	−	4.17148i	0.533044	−	0.142829i	0.0177503	−	0.999842i	$-0.494350\pi$
$853$	15.5682	−	4.17148i	0.533044	−	0.142829i	0.515293	+	0.857014i	$0.327683\pi$
$854$	−2.73749	−	6.60889i	−0.0936751	−	0.226152i
$855$	−17.5509	−	37.7364i	−0.600227	−	1.29056i
$856$	−1.97315	−	1.97315i	−0.0674407	−	0.0674407i
$857$	−30.4354	−	17.5719i	−1.03965	−	0.600245i	−0.119919	−	0.992784i	$-0.538264\pi$
$857$	−30.4354	−	17.5719i	−1.03965	−	0.600245i	−0.919736	+	0.392539i	$0.871597\pi$
$858$	−2.06225	−	1.97616i	−0.0704042	−	0.0674648i
$859$	−42.0847	−	11.2766i	−1.43591	−	0.384751i	−0.544812	−	0.838558i	$-0.683399\pi$
$859$	−42.0847	−	11.2766i	−1.43591	−	0.384751i	−0.891100	+	0.453807i	$0.850066\pi$
$860$	7.08021	+	12.2633i	0.241433	+	0.418174i
$861$	19.7124	−	21.8197i	0.671797	−	0.743613i
$862$	13.3842	−	23.1821i	0.455868	−	0.789587i
$863$	0.834058	−	0.834058i	0.0283917	−	0.0283917i	−0.692768	−	0.721160i	$-0.743609\pi$
$863$	0.834058	−	0.834058i	0.0283917	−	0.0283917i	0.721160	+	0.692768i	$0.243609\pi$
$864$	−2.88035	−	4.32477i	−0.0979913	−	0.147132i
$865$		−	68.0481i		−	2.31370i
$866$	4.95586	−	1.32792i	0.168407	−	0.0451245i
$867$	−28.4463	−	46.9309i	−0.966086	−	1.59386i
$868$	−15.4387	+	20.1202i	−0.524025	+	0.682923i
$869$	−6.39435	+	23.8640i	−0.216913	+	0.809532i
$870$	−8.44746	+	21.6905i	−0.286396	+	0.735377i
$871$	1.46152	−	2.53143i	0.0495218	−	0.0857742i
$872$	−3.51830	−	8.49392i	−0.119145	−	0.287640i
$873$	−20.1697	+	3.53568i	−0.682642	+	0.119665i
$874$	1.24342	+	3.00188i	0.0420593	+	0.101540i
$875$	−9.60841	+	7.37279i	−0.324824	+	0.249246i
$876$	15.9633	+	8.76815i	0.539350	+	0.296248i
$877$	−5.17655	−	8.96605i	−0.174800	−	0.302762i	0.765292	−	0.643683i	$-0.222594\pi$
$877$	−5.17655	−	8.96605i	−0.174800	−	0.302762i	−0.940092	+	0.340921i	$0.889261\pi$
$878$	−4.97140	−	37.7615i	−0.167777	−	1.27439i
$879$	2.74018	−	24.9054i	0.0924240	−	0.840037i
$880$	3.74986	+	4.88692i	0.126408	+	0.164738i
$881$	−33.3264	+	33.3264i	−1.12280	+	1.12280i	−0.131476	+	0.991319i	$0.541972\pi$
$881$	−33.3264	+	33.3264i	−1.12280	+	1.12280i	−0.991319	+	0.131476i	$0.958028\pi$
$882$	−0.0415001	+	0.0795268i	−0.00139738	+	0.00267781i
$883$	6.26658	+	2.59570i	0.210887	+	0.0873524i	0.485626	−	0.874166i	$-0.338592\pi$
$883$	6.26658	+	2.59570i	0.210887	+	0.0873524i	−0.274739	+	0.961519i	$0.588592\pi$
$884$	−3.14727	+	5.45122i	−0.105854	+	0.183344i
$885$	−0.736444	−	34.5424i	−0.0247553	−	1.16113i
$886$	12.6000	−	7.27459i	0.423304	−	0.244394i
$887$	3.77248	+	28.6548i	0.126667	+	0.962134i	0.930246	+	0.366936i	$0.119593\pi$
$887$	3.77248	+	28.6548i	0.126667	+	0.962134i	−0.803579	+	0.595198i	$0.797074\pi$
$888$	−5.70900	−	9.41875i	−0.191581	−	0.316072i
$889$	−4.34147	+	32.9768i	−0.145608	+	1.10601i
$890$	18.7370	−	7.76111i	0.628065	−	0.260153i
$891$	−7.56730	−	14.6079i	−0.253514	−	0.489382i
$892$			13.7289i			0.459679i
$893$	−12.3123	−	45.9503i	−0.412017	−	1.53767i
$894$	−19.6889	+	3.02033i	−0.658495	+	0.101015i
$895$	−21.7251	−	16.6702i	−0.726188	−	0.557224i
$896$	−2.62871	+	0.346077i	−0.0878191	+	0.0115616i
$897$	1.14917	+	0.447550i	0.0383697	+	0.0149433i
$898$	−1.93065	+	3.34398i	−0.0644265	+	0.111590i
$899$	−14.5982	−	35.2433i	−0.486878	−	1.17543i
$900$	16.9034	+	8.82086i	0.563448	+	0.294029i
$901$			100.374i			3.34396i
$902$	11.3899	+	2.69597i	0.379242	+	0.0897661i
$903$	−19.1820	−	2.11048i	−0.638338	−	0.0702323i
$904$	−0.368300	+	1.37451i	−0.0122495	+	0.0457156i
$905$	−25.0513	−	19.2226i	−0.832734	−	0.638980i
$906$	9.56945	+	1.05287i	0.317924	+	0.0349791i
$907$	−2.86236	−	10.6825i	−0.0950430	−	0.354705i	0.901983	−	0.431772i	$-0.142111\pi$
$907$	−2.86236	−	10.6825i	−0.0950430	−	0.354705i	−0.997026	+	0.0770663i	$0.975445\pi$
$908$	−7.20709	−	2.98527i	−0.239176	−	0.0990698i
$909$	41.6608	−	7.30299i	1.38180	−	0.242225i
$910$	−5.69943	+	5.69943i	−0.188934	+	0.188934i
$911$	−25.5918	+	6.85729i	−0.847893	+	0.227192i	−0.656505	−	0.754322i	$-0.727966\pi$
$911$	−25.5918	+	6.85729i	−0.847893	+	0.227192i	−0.191389	+	0.981514i	$0.561299\pi$
$912$	2.86851	+	6.52804i	0.0949860	+	0.216165i
$913$	14.3787	+	11.0332i	0.475866	+	0.365145i
$914$	13.2501	−	17.2679i	0.438275	−	0.571171i
$915$	3.75053	−	15.2940i	0.123989	−	0.505605i
$916$	−1.35179	−	1.76168i	−0.0446643	−	0.0582076i
$917$	−17.8596	+	43.1169i	−0.589776	+	1.42384i
$918$	−27.2943	+	23.8642i	−0.900847	+	0.787635i
$919$	−0.193684	+	0.467594i	−0.00638905	+	0.0154245i	−0.927042	−	0.374958i	$-0.877657\pi$
$919$	−0.193684	+	0.467594i	−0.00638905	+	0.0154245i	0.920653	+	0.390382i	$0.127657\pi$
$920$	−2.30332	−	1.32982i	−0.0759383	−	0.0438430i
$921$	14.2810	+	23.5610i	0.470576	+	0.776361i
$922$	−6.31075	+	23.5520i	−0.207833	+	0.775645i
$923$	0.144772	−	0.540295i	0.00476522	−	0.0177840i
$924$	−8.39269	+	0.178932i	−0.276099	+	0.00588644i
$925$	34.9995	+	20.2069i	1.15078	+	0.664400i
$926$	−10.8146	+	26.1088i	−0.355391	+	0.857990i
$927$	8.98592	+	8.25062i	0.295136	+	0.270986i
$928$	1.52620	−	3.68456i	0.0500998	−	0.120952i
$929$	−24.7259	−	32.2234i	−0.811229	−	1.05721i	−0.997209	−	0.0746608i	$-0.976213\pi$
$929$	−24.7259	−	32.2234i	−0.811229	−	1.05721i	0.185980	−	0.982554i	$-0.440454\pi$
$930$	−53.6057	+	15.5956i	−1.75780	+	0.511399i
$931$	0.0749368	−	0.0976595i	0.00245595	−	0.00320066i
$932$	−3.82188	−	2.93263i	−0.125190	−	0.0960614i
$933$	−34.4979	−	3.79559i	−1.12941	−	0.124262i
$934$	−13.7163	+	3.67528i	−0.448812	+	0.120259i
$935$	30.3912	−	30.3912i	0.993899	−	0.993899i
$936$	2.54224	+	0.928181i	0.0830959	+	0.0303385i
$937$	45.4140	+	18.8111i	1.48361	+	0.614532i	0.969916	−	0.243441i	$-0.0782762\pi$
$937$	45.4140	+	18.8111i	1.48361	+	0.614532i	0.513695	+	0.857973i	$0.328276\pi$
$938$	−2.22350	−	8.29822i	−0.0725999	−	0.270947i
$939$	11.3012	+	25.7187i	0.368799	+	0.839298i
$940$	30.8928	+	23.7048i	1.00761	+	0.773167i
$941$	−1.93768	+	7.23152i	−0.0631665	+	0.235741i	−0.990290	−	0.139014i	$-0.955607\pi$
$941$	−1.93768	+	7.23152i	−0.0631665	+	0.235741i	0.927124	+	0.374755i	$0.122273\pi$
$942$	10.7019	−	14.5803i	0.348687	−	0.475051i
$943$	−4.98896	+	0.806537i	−0.162463	+	0.0262645i
$944$			5.91953i			0.192664i
$945$	−41.6688	+	20.4712i	−1.35549	+	0.665927i
$946$	−2.93952	−	7.09664i	−0.0955721	−	0.230732i
$947$	−5.34388	+	9.25588i	−0.173653	+	0.300776i	−0.939694	−	0.342016i	$-0.888890\pi$
$947$	−5.34388	+	9.25588i	−0.173653	+	0.300776i	0.766041	+	0.642791i	$0.222224\pi$
$948$	−3.54960	−	23.1390i	−0.115286	−	0.751520i
$949$	−9.40490	+	1.23818i	−0.305296	+	0.0401930i
$950$	−20.7575	−	15.9278i	−0.673464	−	0.516767i
$951$	−9.65601	+	24.7937i	−0.313118	+	0.803991i
$952$	4.78813	+	17.8695i	0.155184	+	0.579155i
$953$			31.1380i			1.00866i	0.863511	+	0.504329i	$0.168260\pi$
$953$			31.1380i			1.00866i	−0.863511	+	0.504329i	$0.831740\pi$
$954$	42.5087	−	7.45162i	1.37627	−	0.241255i
$955$	60.4039	−	25.0201i	1.95462	−	0.809632i
$956$	2.68086	−	20.3632i	0.0867052	−	0.658591i
$957$	6.07892	−	11.0673i	0.196504	−	0.357755i
$958$	3.02116	+	22.9480i	0.0976092	+	0.741416i
$959$	−26.3146	+	15.1928i	−0.849744	+	0.490600i
$960$	−5.11575	−	2.80992i	−0.165110	−	0.0906899i
$961$	30.2457	−	52.3871i	0.975668	−	1.68991i
$962$	5.29985	+	2.19527i	0.170874	+	0.0707783i
$963$	7.42161	+	3.87288i	0.239158	+	0.124802i
$964$	7.67223	−	7.67223i	0.247106	−	0.247106i
$965$	7.69814	+	10.0324i	0.247812	+	0.322955i
$966$	3.31833	−	1.45812i	0.106766	−	0.0469143i
$967$	3.51312	+	26.6848i	0.112974	+	0.858124i	0.950282	+	0.311392i	$0.100795\pi$
$967$	3.51312	+	26.6848i	0.112974	+	0.858124i	−0.837307	+	0.546732i	$0.815871\pi$
$968$	3.82930	+	6.63253i	0.123078	+	0.213178i
$969$	42.5467	−	25.7889i	1.36680	−	0.828459i
$970$	−18.2482	+	14.0024i	−0.585916	+	0.449589i
$971$	−12.9457	−	31.2537i	−0.415448	−	1.00298i	−0.983650	−	0.180091i	$-0.942361\pi$
$971$	−12.9457	−	31.2537i	−0.415448	−	1.00298i	0.568202	−	0.822889i	$-0.307639\pi$
$972$	12.1328	+	9.78754i	0.389159	+	0.313935i
$973$	10.0798	+	24.3348i	0.323144	+	0.780138i
$974$	18.9288	−	32.7857i	0.606518	−	1.05052i
$975$	−9.81589	+	1.50579i	−0.314360	+	0.0482238i
$976$	−0.698289	+	2.60605i	−0.0223517	+	0.0834176i
$977$	−5.53898	+	7.21854i	−0.177208	+	0.230942i	−0.873509	−	0.486808i	$-0.838161\pi$
$977$	−5.53898	+	7.21854i	−0.177208	+	0.230942i	0.696301	+	0.717750i	$0.254828\pi$
$978$	2.14001	−	0.0456251i	0.0684301	−	0.00145893i
$979$	−10.6265	+	2.84735i	−0.339623	+	0.0910018i
$980$			0.100761i			0.00321870i
$981$	17.7078	+	21.1462i	0.565365	+	0.675146i
$982$	−16.7259	+	16.7259i	−0.533744	+	0.533744i
$983$	−4.20694	+	7.28664i	−0.134181	+	0.232408i	−0.925284	−	0.379275i	$-0.876174\pi$
$983$	−4.20694	+	7.28664i	−0.134181	+	0.232408i	0.791104	+	0.611682i	$0.209507\pi$
$984$	−10.9082	+	2.00293i	−0.347740	+	0.0638510i
$985$	36.1415	+	62.5989i	1.15156	+	1.99457i
$986$	−26.8788	−	7.20214i	−0.855994	−	0.229363i
$987$	−50.9541	+	14.8241i	−1.62189	+	0.471857i
$988$	−3.21630	−	1.85693i	−0.102324	−	0.0590770i
$989$	2.34519	+	2.34519i	0.0745727	+	0.0745727i
$990$	−15.1269	−	10.6145i	−0.480764	−	0.337352i
$991$	−21.2211	−	51.2322i	−0.674110	−	1.62745i	−0.774558	−	0.632503i	$-0.782028\pi$
$991$	−21.2211	−	51.2322i	−0.674110	−	1.62745i	0.100448	−	0.994942i	$-0.467972\pi$
$992$	9.23919	−	2.47563i	0.293345	−	0.0786015i
$993$	−39.8727	−	15.5286i	−1.26532	−	0.492785i
$994$	−0.821984	−	1.42372i	−0.0260718	−	0.0451576i
$995$	33.0485	−	43.0696i	1.04771	−	1.36540i
$996$	−16.6789	−	4.09014i	−0.528492	−	0.129601i
$997$	−36.6923	−	4.83064i	−1.16206	−	0.152988i	−0.475266	−	0.879842i	$-0.657648\pi$
$997$	−36.6923	−	4.83064i	−1.16206	−	0.152988i	−0.686792	+	0.726854i	$0.740982\pi$
$998$	−20.6450	−	8.55145i	−0.653507	−	0.270691i
$999$	24.8093	+	21.8231i	0.784932	+	0.690452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.v.a.137.3	✓	168
9.5	odd	6		738.2.v.b.383.13	yes	168
41.3	odd	8		738.2.v.b.659.13	yes	168
369.167	even	24	inner	738.2.v.a.167.3	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.v.a.137.3	✓	168	1.1	even	1	trivial
738.2.v.a.167.3	yes	168	369.167	even	24	inner
738.2.v.b.383.13	yes	168	9.5	odd	6
738.2.v.b.659.13	yes	168	41.3	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.v (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.68221 - 0.412525i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.872167 - 3.25497i) q^{5} +(-0.0369189 - 1.73166i) q^{6} +(2.62871 + 0.346077i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.65965 + 1.38791i) q^{9} +3.36980 q^{10} +(-1.81231 - 0.238596i) q^{11} +(1.66310 - 0.483847i) q^{12} +(-0.549181 + 0.715707i) q^{13} +(0.346077 + 2.62871i) q^{14} +(-2.80992 + 5.11575i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-6.44629 - 2.67014i) q^{17} +(-0.652247 + 2.92824i) q^{18} +(1.57542 - 3.80341i) q^{19} +(0.872167 + 3.25497i) q^{20} +(-4.27928 - 1.66658i) q^{21} +(-0.238596 - 1.81231i) q^{22} +(0.394630 + 0.683520i) q^{23} +(0.897801 + 1.48120i) q^{24} +(-5.50404 - 3.17776i) q^{25} +(-0.833458 - 0.345230i) q^{26} +(-3.90153 - 3.43192i) q^{27} +(-2.44957 + 1.01465i) q^{28} +(0.520557 - 3.95402i) q^{29} +(-5.66870 - 1.39012i) q^{30} +(8.28363 - 4.78256i) q^{31} +(0.965926 + 0.258819i) q^{32} +(2.95026 + 1.14899i) q^{33} +(0.910736 - 6.91773i) q^{34} +(3.41915 - 8.25455i) q^{35} +(-2.99727 + 0.127862i) q^{36} -6.35886 q^{37} +(4.08156 + 0.537348i) q^{38} +(1.21908 - 0.977417i) q^{39} +(-2.91833 + 1.68490i) q^{40} +(-2.27555 + 5.98514i) q^{41} +(0.502237 - 4.56481i) q^{42} +(4.05897 - 1.08760i) q^{43} +(1.68881 - 0.699527i) q^{44} +(6.83725 - 7.44659i) q^{45} +(-0.558092 + 0.558092i) q^{46} +(9.16755 - 7.03451i) q^{47} +(-1.19836 + 1.25057i) q^{48} +(0.0288824 + 0.00773902i) q^{49} +(1.64493 - 6.13896i) q^{50} +(9.74251 + 7.15099i) q^{51} +(0.117751 - 0.894411i) q^{52} +(-5.50514 - 13.2906i) q^{53} +(2.30519 - 4.65684i) q^{54} +(-2.35726 + 5.69094i) q^{55} +(-1.61407 - 2.10349i) q^{56} +(-4.21919 + 5.74823i) q^{57} +(3.95402 - 0.520557i) q^{58} +(-5.12647 + 2.95977i) q^{59} +(-0.124409 - 5.83533i) q^{60} +(-2.60605 + 0.698289i) q^{61} +(6.76356 + 6.76356i) q^{62} +(6.51113 + 4.56885i) q^{63} +1.00000i q^{64} +(1.85063 + 2.41179i) q^{65} +(-0.346257 + 3.14712i) q^{66} +(-3.21244 + 0.422926i) q^{67} +(6.91773 - 0.910736i) q^{68} +(-0.381881 - 1.31262i) q^{69} +(8.85823 + 1.16621i) q^{70} +(-0.572841 + 0.237279i) q^{71} +(-0.899257 - 2.86205i) q^{72} +(7.43536 + 7.43536i) q^{73} +(-1.64579 - 6.14219i) q^{74} +(7.94804 + 7.61621i) q^{75} +(0.537348 + 4.08156i) q^{76} +(-4.68148 - 1.25440i) q^{77} +(1.25963 + 0.924571i) q^{78} +(1.76414 - 13.4000i) q^{79} +(-2.38281 - 2.38281i) q^{80} +(5.14744 + 7.38268i) q^{81} +(-6.37016 - 0.648940i) q^{82} +(-8.58655 - 4.95745i) q^{83} +(4.53925 - 0.696335i) q^{84} +(-14.3135 + 18.6537i) q^{85} +(2.10108 + 3.63918i) q^{86} +(-2.50682 + 6.43674i) q^{87} +(1.11279 + 1.45021i) q^{88} +(5.56027 - 2.30314i) q^{89} +(8.96246 + 4.67696i) q^{90} +(-1.69133 + 1.69133i) q^{91} +(-0.683520 - 0.394630i) q^{92} +(-15.9077 + 4.62805i) q^{93} +(9.16755 + 7.03451i) q^{94} +(-11.0060 - 8.44518i) q^{95} +(-1.51812 - 0.833856i) q^{96} +(-5.41524 + 4.15526i) q^{97} +0.0299013i q^{98} +(-4.48897 - 3.14990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 4 q^{3} - 12 q^{7} - 4 q^{9} + 8 q^{15} + 84 q^{16} - 12 q^{17} - 8 q^{21} - 12 q^{22} + 48 q^{25} - 40 q^{27} + 16 q^{30} - 64 q^{33} - 36 q^{34} + 24 q^{35} - 4 q^{36} + 32 q^{39} - 32 q^{42}+ \cdots + 68 q^{99}+O(q^{100}) \) 168 * q - 4 * q^3 - 12 * q^7 - 4 * q^9 + 8 * q^15 + 84 * q^16 - 12 * q^17 - 8 * q^21 - 12 * q^22 + 48 * q^25 - 40 * q^27 + 16 * q^30 - 64 * q^33 - 36 * q^34 + 24 * q^35 - 4 * q^36 + 32 * q^39 - 32 * q^42 + 12 * q^44 + 72 * q^45 - 12 * q^47 - 8 * q^48 + 12 * q^49 - 44 * q^51 + 12 * q^56 - 64 * q^57 - 24 * q^58 - 108 * q^61 + 48 * q^63 - 84 * q^65 - 4 * q^66 - 60 * q^67 + 40 * q^69 + 12 * q^70 + 20 * q^75 - 60 * q^79 + 68 * q^81 + 12 * q^82 - 120 * q^83 + 8 * q^84 + 24 * q^85 + 72 * q^89 + 40 * q^90 - 16 * q^93 - 12 * q^94 - 120 * q^95 + 96 * q^97 + 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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